Thermal Physics: Key Concepts And Applications

Thermal Physics

It is the study of heat, temperature, and the laws governing the conversion of heat into other forms of energy. It explores how thermal energy affects matter, from the expansion of solids, liquids, and gases to phase changes involving latent heat. Key topics include calorimetry, modes of heat transfer (conduction, convection, and radiation), and the behavior of ideal gases. The subject also delves into thermodynamic principles such as the first and second laws, the concept of reversible and irreversible processes, and the working of engines like the Carnot engine.

1.0Thermal Expansion of Solids, Liquids, and Gases

Thermal Expansion

Thermal Expansion occurs when matter is heated without a change in state, leading to an increase in size.
According to the atomic theory of matter, thermal expansion is due to the asymmetry of the potential energy curve between atoms.
As temperature increases (from $T_{1} t o T_{2}$ ), atomic vibration amplitude and energy (from $E_{1} t o E_{2}$ ) increase, causing the average interatomic distance to grow (from $r_{1} t o r_{2}$ ) .
This increase in distance leads to the overall expansion of matter. If the potential energy curve were symmetric, no expansion would occur upon heating.
Solids exhibit minimal thermal expansion due to strong intermolecular forces, while gases expand the most due to weak intermolecular forces.
Solids can expand:
In one dimension → Linear expansion
In two dimensions → Superficial expansion
In three dimensions → Volumetric expansion
Liquids and gases primarily undergo volume expansion.

2.0Potential Energy V/s Distance Curve

Heating matter usually causes it to expand.
According to atomic theory, thermal expansion is due to asymmetry in the potential energy curve.
As temperature rises the amplitude of atomic vibrations and their energy increases
This results in an increase in the average distance between atoms .
If the potential energy curve were symmetrical, no thermal expansion would occur.

$T_{2} > T_{2}, E_{2} > E_{1}, r_{2} a vg . > r_{1} a vg .$

3.0Linear Expansion

When the rod is heated, its increase in length ΔL is proportional to its original length L0 and change in temperature ΔT where ΔT is in °C or K.

$L = L_{0} (1 + α Δ T)$ where L is the length after heating the rod.

Note:Thermal expansion is typically a 3-D phenomenon. However, when the other two dimensions of an object are negligible compared to one, the expansion is significant only in that dimension, and this is referred to as linear expansion.

4.0Superficial (Areal) Expansion

When the temperature of a 2D object is changed, its area changes, then the expansion is called superficial expansion.

$A = A_{0} (1 + β Δ T) β = 2 α$

5.0Volume Expansion

When a solid is heated and its volume increases, then the expansion is called volume or cubical expansion.

$V = V_{0} (1 + γ Δ T) γ = 3 α α : β : γ = 1 : 2 : 3 U ni t o f α, β, γi s 1 /^{\circ} C or 1/ K K^{- 1}$

6.0Variation of Time Period of Pendulum Clocks

A pendulum clock's time is based on the pendulum's oscillations.
The second hand advances by one second when the pendulum reaches its extreme position.
The second hand moves by two seconds for each complete oscillation.
A pendulum with a 2-second time period is called a "seconds pendulum."

Therefore change (loss or gain) in time per unit time lapsed is $\frac{T - T ^{'}}{T} = \frac{1}{2} α Δ θ$

Gain or loss in time in duration of 't' in $Δ T = \frac{1}{2} α Δ θT$ if T is the correct time then

<0,T<T'clock becomes fast and gain time
>0,T'>Tclock becomes slow and loose time

7.0Measurement of Length by Metallic Scale

Case (i) : When object is expanded only; No expansion of scale

$l_{2} = l_{1} {1 + α (θ_{2} - θ_{1})}$

Case (ii) : When only the measurement instrument is expanded, the actual length of the object will not change but the measured value (MV) decreases.

$M V = l_{1} {1 + α (θ_{s} - θ_{1})}$

Case (iii): If both expanded simultaneously

$M V = l_{1} {1 + (α_{0} - α_{s}) (θ_{2} - θ_{1})}$

8.0Thermal Stress of a Material

When the temperature of the rod is decreased or increased under constrained conditions, compressive or tensile stresses are developed in the rod. These stresses are known as thermal stresses.

$Strain = \frac{Δ L}{L _{0}} = \frac{Final Length - Original Length}{Original Length} = α Δ T$

original length refers to the natural length of rod at new temperature.

9.0The Bimetallic Strip

A bimetallic strip is made of two metals with different coefficients of linear expansion (e.g., brass and steel).
Brass $(α = 19 \times 1 0^{- 6} /^{\circ} C)$ has a higher expansion coefficient than steel (α = 12 × 10⁻⁶ /°C).
The metals are joined together by welding or riveting.
When heated up , the brass expands more than the steel, causing the strip to bend.
The brass side of the strip has a larger radius than the steel side.
Upon cooling, the strip bends in the opposite direction.

Upon cooling, the strip bends in the opposite direction.

10.0Thermal Expansion in Liquids

Liquids experience volume expansion instead of linear or superficial expansion.
Initially, as both the liquid and vessel are heated, the liquid level falls due to the vessel expanding more than the liquid.
Later, the liquid level rises as the liquid expands faster than the vessel.
The actual increase in the liquid's volume is the sum of the apparent volume increase and the vessel's volume increase.

$γ_{r} = \frac{Real increase in volume}{Initial Volume \times Δ θ} = \frac{( Δ V )}{V \times Δ θ}$

Co-Efficient of expansion of flask

$γ_{Vessel} = \frac{( Δ V ) _{Vessel}}{V \times Δ θ} γ_{real} = γ_{Apparent} + γ_{Vessel}$

11.0Variation of Density with Temperature

Mass of substance does not change with change in temperature so with increase of temperature, volume increases so density decreases and vice-versa.

$d = \frac{d _{0}}{( 1 + γ Δ T )} For solids values of are generally small d = d_{0} (1 - γ Δ T)$

Anomalous expansion of water

Water's density increases from 0°C to 4°C, making negative; from 4°C onward, is positive.
At 4°C, water's density is maximum.
This causes ice to form at the surface of lakes in cold weather.
As winter approaches, surface water cools, becomes denser, and sinks, leading to the formation of ice at 0°C.
Ice on the surface slows further freezing, as ice is a poor heat conductor.
Aquatic life survives winter because the lake bottom remains at around 4°C, unfrozen.

12.0Variation of Force of Buoyancy with Temperature

$F_{B}^{'} = F_{B} = [1 + (γ - γ_{1}) Δ θ]$

13.0Calorimetry and Latent Heat

Calorimetry

When two bodies at different temperatures come into contact, heat flows from the hotter to the cooler body until they reach thermal equilibrium.

Heat Lost = Heat Gained (Principle of calorimetry)

The principle of calorimetry represents the law of conservation of heat energy.

$m_{1} s_{1} Δ T_{1} = m_{2} s_{2} Δ T_{2} m_{1} s_{1} (T_{1} - T_{mix}) = m_{2} s_{2} (T_{mix} - T_{2}) (s= specific heat) T_{1} > T_{mix} > T_{2}$

Water Equivalent

The water equivalent of a body is the mass of water (W in grams) that would absorb or release the same amount of heat as the body does when its temperature changes by the same amount.

$(H_{c})_{substance} = (H_{c})_{water} M_{s} S_{s} = M_{w} S_{w} M_{s} S_{s} = W \times 1 cal / g^{\circ} C Water Equivalent = W in gram$

Numerically water equivalent and heat capacity are same but their unit is different.

Numerically water equivalent and heat capacity are same but their unit is different.

Note : whenever water equivalent or heat capacity of container is given in that case heat consumed by container will also be calculated.

Latent Heat

The heat required for a phase or state change, $Q = m L \Rightarrow L = \frac{Q}{m}, L = latent heat U ni t : S I \to J / k g or CGS \to c a l / g$

(1)Latent heat (L): The heat supplied to a substance of unit mass that causes a change in its state at a constant temperature.

(2)Latent heat of Fusion (Lf): The heat supplied to a substance that changes it from solid to liquid at its melting point and 1 atm pressure is called the latent heat of fusion. For ice, the latent heat of fusion is 80 kcal/kg.

(3) Latent heat of vaporization (Lv):The heat supplied to a substance that changes it from liquid to vapor at its boiling point and 1 atm pressure is called the latent heat of vaporization. For water, the latent heat of vaporization is 540 kcal/kg.

Heating Curve

14.0Heat Conduction in One Dimension

Conduction

Conduction, or thermal Conduction, is a process of heat transfer in which heat is transferred from one particle to another without dislocating the particle from its equilibrium position.
Transient State : In this state, the temperature of each part of the rod varies with time.
Steady state : After a long time, when any part absorbs no heat, the temperature of every part is constant and decreases uniformly from the hotter end to the colder end.

Note:In steady state, each point has a different temperature but remains constant.

15.0Fourier’s Law of Heat Conduction

$i_{T} = \frac{d Q}{d t} = \frac{K A}{l} (\frac{d T}{d x})$

K= Coefficient of Thermal Conductivity

16.0Series Combination

$In Series Combination R_{e q} = R_{1} + R_{2} \Rightarrow \frac{( L _{1} + L _{2} )}{K _{eq} A = \frac{L _{1}}{K _{1} A} + \frac{L _{2}}{K _{2} A} Equivalent Thermal Conductivity is K _{eq} = \frac{L _{1} + L _{2}}{\frac{L _{1}}{L _{2}} + \frac{K _{1}}{K _{2}}} = \frac{Σ L _{i}}{Σ} \frac{L _{i}}{K _{i}}} If lengths of the rod are the same then (L_{1} = L_{2} = L) K_{e} q = \frac{2 K _{1} K _{2}}{K _{1} + K _{2}}$

17.0Parallel Combination

$In Parallel Combination K_{eq} = \frac{2 K _{1} K _{2}}{K _{1} + K _{2}} \frac{1}{R _{eq}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} \Rightarrow \frac{K _{1} A _{1}}{L _{1}} + \frac{K _{2} A _{2}}{L _{2}} \Rightarrow \frac{K _{1} A}{L} + \frac{K _{2} A}{L} = \frac{Σ ( K A )}{L} \Rightarrow K_{eq} = \frac{K _{1} A _{1}}{L _{1}} + \frac{K _{2} A _{2}}{L _{2}}, Σ (K A), Σ (A) K_{eq} = \frac{K _{1} + K _{2}}{2}$

18.0Temperature of Junction $(T_{0})$

To determine the temperature at the junction, we equate the heat flow rates through both sections.

$\Rightarrow (\frac{d θ}{d t})_{1} = (\frac{d θ}{d t})_{2} \Rightarrow \frac{K _{1} A}{L _{1}} (T_{1} - T_{0}) = \frac{K _{2} A}{L _{2}} (T_{0} - T_{2}) \Rightarrow T_{0} = \frac{K _{1} L _{2} T _{1} + K _{2} L _{1} T _{2}}{K _{2} L _{1} + K _{1} L _{2}}$

Growth of Ice on Lake

$t \propto (x_{2}^{2} - x_{1}^{2}) Time taken to double and triple the thickness ratio t_{1} : t_{2} : t_{3} :: 12 : 2^{2} : 3^{2} t_{1} : t_{2} : t_{3} :: 1 : 4 : 9 Ratio of time taken to form thickness (0 \to x) \cdot (x \to 2 x) \cdot (2 x \to 3 x) Δ t_{1} : Δ t_{2} : Δ t_{3} = (x^{2} - 0^{2}) : (2 x^{2} - x^{2}) : (3 x^{2} - 2 x^{2}) Δ t_{1} : Δ t_{2} : Δ t_{3} :: 1 : 3 : 5$

19.0Convection and Radiation

Convection

Convection is the transfer of heat through the actual movement of a heated fluid and requires a medium.
Natural convection occurs due to density differences (e.g., heating a fluid from below).
Forced convection happens when fluid motion is driven by external devices like fans or pumps.

Thermal Radiation

Radiation is the transfer of heat without requiring a material medium.
It allows heat to travel through a vacuum, unlike conduction and convection, which need a medium.
A heated object in a vacuum can still lose heat through radiation.
It is the only mode of heat transfer that occurs without heating the intervening space or matter.

20.0Newton’s Law of Cooling

Newton's Law of Cooling asserts that the speed at which an object's temperature changes is directly linked to the disparity between its Temperature.The surrounding ambient Temperature relationship dictates how quickly an object cools or heats as it interacts thermally with its environment.

$T = T_{0} + \frac{e}{- K T} + C$

This equation calculates the time of cooling of a body through a particular range of temperature.

Note-For Numerical Problems (Newton’s Law of Cooling)

$\frac{T _{2} - T _{1}}{t _{2} - t _{1}} = K [\frac{T _{1} + T _{2}}{2} - T_{0}]$

This equation calculates the time of cooling of a body through a particular range of temperature.

21.0Ideal Gas Laws

Charle's Law:This law states that, for a fixed amount of an ideal gas at fixed pressure, the volume is directly proportional to its absolute temperature,

$V \propto T \frac{V _{1}}{V _{2}} = \frac{T _{1}}{T _{2}}$

Graphs for Charles's Law

Here t represents temperature in °C and T represents in K i.e. absolute temperature.

Boyle's Law : This law states that, for a fixed amount of an ideal gas at fixed temperature, the volume is inversely proportional to its pressure.

$V \propto \frac{1}{P} P_{1} V_{1} = P_{2} V_{2}$

Graphs for Boyle’s Law

Gay–Lussac's Law: According to this law, for a given mass of an ideal gas; at fixed volume, pressure of a gas is directly proportional to its absolute temperature,

$V \propto T \frac{P _{1}}{T _{1}} = \frac{P _{2}}{T _{2}}$

Graph for Gay–Lussac's Law

Here t represents temperature in °C and T represents in K i.e. absolute temperature.

Avogadro's Law:This law states that, at the same temperature and pressure, equal volumes of all gases contain an equal number of molecules, i.e., $N_{1} = N_{2}$ if P, V and T are the same.

5.Dalton's Partial Pressure Mixture Law : The total pressure of a non-reactive gas mixture equals the sum of the partial pressures of its components.

$P = P_{1} + P_{2} + P_{3} + ..................$

22.0Specific Heats

The amount of energy required to elevate the temperature of the unit mass of a substance by 1°C (or 1K) is called its specific heat. It is represented by s or c.

$c = \frac{1}{m} \frac{d Q}{d t}$

(1) Gram specific heat :The amount of energy required to elevate the temperature of 1 gram of a substance by 1°C (or 1K) is called its specific heat.

$c_{gram} = \frac{1}{m} \frac{Q}{Δ t} U ni t : j o u l e / k g^{\circ} C, c a l / g^{\circ} C$

(2)Molar specific heat :The amount of energy required to elevate the temperature of 1 mole of a substance by 1°C (or 1K) is called its specific heat.

$c_{molar} = \frac{1}{μ} \frac{Q}{Δ t} U ni t : j o u l e / m o l^{\circ} C, c a l / m o l^{\circ} C$

Note

The value of specific heats of gas can vary from zero (0) to infinity.
Generally two types of specific heats are defined for a gas –

(a) Specific heat at constant volume ( $c_{v}$ )

(b) Specific heat at constant pressure ( $c_{p}$ )

There are many possible processes to give heat to a gas.

A specific heat can be associated with each such process which depends on the nature of the process.

(1) Isochoric Process

V = Constant

$c_{V} = \frac{1}{μ} \frac{Q}{Δ t}$

(2) Isobaric Process

P= Constant

$c_{P} = \frac{1}{μ} \frac{Q}{Δ t}$

(3) Isothermal Process

T=Constant

$c_{Isothermal} = \infty$

(4) Adiabatic Process

Q=0

$c_{Adiabatic} = 0$

23.0Mayer’s Law

$For an ideal gas c_{v} = \frac{f}{2} R c_{v} = (\frac{f + 1}{2}) R c_{p} - c_{v} = R If gram specific heat are given (c_{p})_{gram} - (c_{v})_{gram} = \frac{R}{M _{w}}$

24.0Different Thermodynamic Process

Isochoric Process

$Volume= Constant Equation of state \Rightarrow \frac{P}{T} = constant W or k d o n e w = \int_{V_{i}}^{V_{f}} P, d V = 0 (b ec a u se d V = 0) Form of First Law, Q = Δ U = μ c_{v} Δ T Slope of the P-V curve \frac{d P}{d V} = \infty$

Isobaric Process

$Pressure = constant Equation of state \frac{V}{T} = constant (V \propto T) Work done w = \int_{V_{i}}^{V_{f}} P d V = P (V_{f} - V_{i}) Form of First Law Q = Δ U + P (V_{f} - V_{i}) C_{p} (T_{f} - T_{i}) = μ c_{v} (T_{f} - T_{i}) + P (V_{f} - V_{i}) Slope of the PV curve (\frac{d P}{d V})_{isobaric} = 0$

Isothermal Process

Temperature= constant
Equation of state PV=Constant

$Work done w = μ RT lo g_{e} (\frac{V _{f}}{V _{i}}) = 2.303, μ RT lo g_{10} (\frac{P _{1}}{P _{2}}) Form of First Law Δ U = 0 Slope of isothermal curve (\frac{d P}{d V})_{isothermal} = - \frac{P}{V}$

Adiabatic Process

No heat exchange between system and surroundings
$Work done w = \frac{- 1}{γ - 1} [P_{1} V_{1} - P_{2} V_{2}] = \frac{μ R}{γ - 1} (T_{1} - T_{2}) Slope of adiabatic curve \frac{[}{d P} d V]_{a} d iaba t i c = \frac{- γ P}{V}$

Note-The slope of an adiabatic curve is steeper than that of an isothermal curve.

Polytropic Process

$P V^{x} = Constant, C = C_{v} + \frac{R}{1 - x} For isobaric (x = 0) : C = C_{p} = \frac{R}{γ - 1} + R = C + R For isothermal: x = 1, C = \infty For adiabatic: x = γ, C = 0$

25.0Bulk Modulus of Gases

It is a measure of its resistance to uniform compression. It is defined as the ratio of the infinitesimal change in pressure to the resulting relative change in volume.

$B = - V \frac{d P}{d V}$

For Gases:

The value of bulk modulus depends on how the compression is carried out—whether it's isothermal (constant temperature) or adiabatic (no heat exchange).

1. Isothermal Bulk Modulus: In an isothermal process (constant temperature), using Boyle’s law PV=constant

$B_{i so} = P$

2. Adiabatic Bulk Modulus: In an adiabatic process (no heat exchange), the pressure-volume relation is PV=constant

$B_{a d ia} = γ P$

Note:Adiabatic bulk modulus is always greater because the gas resists compression more when no heat is allowed to escape.

26.0Equivalence of Heat and Work

Both work and heat are forms of energy; however, work represents organized energy transfer, while heat involves disorganized or random energy transfer.
While mechanical work can be fully converted into heat, the reverse process is not possible.
W=JQ (∴ J = Conversion Factor=Joule’s Constant=Mechanical Equivalent of heat)

$J = 4.18 \frac{Joule}{calorie} 1 cal = 4.18 \approx 4.2 Joule$ 1 cal > 1 joule

27.0First Law of Thermodynamics

When heat is supplied to a system capable of performing external work, the absorbed heat equals the sum of the increase in internal energy and the external work done by the system.

$Δ Q = Δ U + Δ W$

FLOT introduces the concept of internal energy.
It is based on conservation of energy principle

28.0Sign Convention used in Physics Thermodynamics

$Δ Q = Δ U + Δ W$

Drawbacks of FLOT

It does not specify how much of the heat is converted into mechanical work.
It does not specify the correct direction of heat flow.

29.0Second Law of Thermodynamics

Kelvin planck statement : It states that in a cyclic process total heat can not be converted into mechanical work.
Claussius statement : A net heat flow from a body at lower temperature to one at higher temperature is impossible.

Carnot Engine and Its Efficiency

It is an ideal reversible heat engine that operates between two temperatures T₁(Source) and T₂(Sink). {T_1(Source) and T_2(Sink).}

It operates through two isothermal and two adiabatic processes called Carnot Cycle. It is a theoretical heat engine with which the efficiency of Practical engines is compared.

Carnot Engine Diagram

Carnot Cycle Diagram

Efficiency of Carnot Engine

It is defined as the ratio of the engine's net work done per cycle to the amount of heat absorbed by the working substance from the source.

$η = \frac{W}{Q _{1}} = \frac{Q _{1} - Q _{2}}{Q _{1}} = 1 - \frac{Q _{2}}{Q _{1}}$

30.0Blackbody Radiation and Related Laws

Ideal Black Body

A body that absorbs all thermal radiation incident on it at low temperatures and emits all absorbed radiation at high temperatures, regardless of wavelength.

Characteristics:

Emission depends only on temperature, not material or surface properties.
Emitted radiation is called full or white radiation.
The spectral energy distribution is continuous across all wavelengths.
If a heat source has a continuous spectrum (e.g., kerosene lamp, filament), it's considered a black body.
For an ideal black body:
Absorptivity (a) = 1
Reflectivity (r) = 0
Transmissivity (t) = 0
Emissivity (e) = 1
Acts as a perfect absorber at low temperatures and a perfect emitter at high temperatures.
Color doesn't define a black body (e.g., the Sun is not black).

Examples:

Wien’s black body
Ferry’s black body

31.0Kirchhoff's Law

At a given temperature, the ratio of a body's spectral emissive power to its spectral absorptive power is constant. This constant is equal to the spectral emissive power of an ideal black body at the same temperature:

$\frac{E _{λ}}{a _{λ}} = Constant = E_{λ}$

Thus, good absorbers are also good emitters, and bad absorbers are bad emitters. According to Kirchhoff's law, the absorptivity of a surface is equal to its emissivity (e=a).

Practical confirmation of Kirchhoff's law was carried out using the Rishi apparatus, with the Leslie container as the primary base.

32.0Stefan's Law

The amount of radiation emitted per second per unit area by a black body is directly proportional to the fourth power of its absolute temperature.

$E = σ T^{4} σ = Stefan’s constant = 5.67 \times 1 0^{- 8} W / m^{2} K^{4}$

Stefan’s Radiation Law

An ideal blackbody absorbs all radiation that falls on it, including visible, infrared, ultraviolet, and all other wavelengths.
A blackbody is both a perfect absorber and a perfect emitter of radiation.
It emits more radiant power per unit area than any real object at the same temperature.
The rate of radiation emitted per unit area is proportional to the fourth power of the absolute temperature.

$P = σ A T^{4} Rate of Emission of Radiation \frac{d Q}{d t} = e A σ (T_{b}^{4} - T_{s}^{4}) = m s \frac{d T}{d t}$

33.0Spectral Emissive Power

$\int_{0}^{\infty} E_{λ} d λ = Total emissive power Total area of graph = Total emissive power = e σ T^{4}$

Spectral Energy Distribution Curve of Black Body Radiations

Spectral energy distribution curves are continuous, indicating that radiation is emitted at all wavelengths (from 0 to ∞) at any given temperature, though the intensity varies across different wavelengths.

As the wavelength increases, the amount of emitted radiation initially increases, reaches a maximum, and then decreases.
The area under the spectral energy curve at a specific temperature represents the body's spectral emissive power.

34.0Wein's Displacement Law

The wavelength corresponding to maximum emission of radiation decreases with increasing temperature.

$[λ_{m} \propto \frac{1}{T}] λ_{m} T = b \Rightarrow λ_{m 1} T_{1} = λ_{m 2} T_{2} = b Wien’s Constant = 2.89 \times 1 0^{- 3} mK$

35.0Related Qustions

Q-1.A body is floating over liquid if we increases temperature then what changes occur in Buoyancy force.(Assume body is always in floating condition)

Solution:

A body is floating over liquid if we increases temperature then what changes occur in Buoyancy force.(Assume body is always in floating condition)

Body is in equilibrium

So, mg = B

and gravitational force does not change with change in temperature. So, Buoyancy force remains constant.

By increasing temperature density of liquid decreases so volume of body inside the liquid increases to keep the Buoyance force constant for equal to gravitational force)

Q-2.On increasing temperature by T.How much volume of liquid will overflow ?

(If the container is initially filled up to the brim.)

Solution:

$V_{overflow} = Δ V_{liquid} - Δ V_{vessel} V_{overflow} = V_{0} γ_{L} Δ T - V_{0} γ_{V} Δ T V_{overflow} = V_{0} (γ_{L} - γ_{V}) Δ T$

On increasing temperature by T.How much volume of liquid will overflow ? (If the container is initially filled up to the brim.)

Q-3.If volume of metal increases by 0.12% on increasing temperature by 20°C. Find ?

Solution:

$γ = \frac{Δ V}{V Δ T} \frac{Δ V}{V} = \frac{0.12}{100} = 12 \times 1 0^{- 4} 3 α = \frac{12 \times 1 0 ^{- 4}}{20} \Rightarrow α = \frac{1}{5} \times 1 0^{- 4} = 0.2 \times 1 0^{- 4}$

Q-4.Heat is supplied at a constant rate to ice and its temperature remains constant for 5 min. After that temperature started increasing at a rate of 2°C/min.Find $\frac{L _{F u s i o n}}{s _{w a t er}}$ ?

Solution:

Let rate of heat supply = P

$P \times 5 = m L ...........(1) \frac{Δ Q}{Δ t} = m s_{water} \frac{Δ T}{Δ t} P = m s_{water} \times 2 ...........(2) Solving equation (1) and (2) \frac{L _{fusion}}{s _{water}} = 10$

Q-5.Specific heat of a substance depends on temperature as $s = 3 T^{2}$ , where temperature is in kelvin and the constant 3 is in SI units. Find heat required to raise the temperature of unit mass from 2K to 5K ?

Solution:

$\int d Q = \int m s d T Δ Q = \int_{2}^{5} 3 T^{2} d T Δ Q = [T^{3}]_{2}^{5} = 5^{3} - 2^{3} = 125 - 8 = 117 J$

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Thermal Physics

1.0Thermal Expansion of Solids, Liquids, and Gases

Thermal Expansion

2.0Potential Energy V/s Distance Curve

3.0Linear Expansion

4.0Superficial (Areal) Expansion

5.0Volume Expansion

6.0Variation of Time Period of Pendulum Clocks

7.0Measurement of Length by Metallic Scale

8.0Thermal Stress of a Material

9.0The Bimetallic Strip

10.0Thermal Expansion in Liquids

11.0Variation of Density with Temperature

12.0Variation of Force of Buoyancy with Temperature

13.0Calorimetry and Latent Heat

Calorimetry

Latent Heat

14.0Heat Conduction in One Dimension

15.0Fourier’s Law of Heat Conduction

16.0Series Combination

17.0Parallel Combination

18.0Temperature of Junction (T0​)

19.0Convection and Radiation

20.0Newton’s Law of Cooling

21.0Ideal Gas Laws

22.0Specific Heats

23.0Mayer’s Law

24.0Different Thermodynamic Process

25.0Bulk Modulus of Gases

For Gases:

26.0Equivalence of Heat and Work

27.0First Law of Thermodynamics

28.0Sign Convention used in Physics Thermodynamics

29.0Second Law of Thermodynamics

30.0Blackbody Radiation and Related Laws

Ideal Black Body

31.0Kirchhoff's Law

32.0Stefan's Law

33.0Spectral Emissive Power

34.0Wein's Displacement Law

35.0Related Qustions

Table of Contents

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18.0Temperature of Junction $(T_{0})$