Home
Class 11
PHYSICS
A heat engine operates between a cold re...

A heat engine operates between a cold reservoir at temperature `T_(2) = 300 K` and a hot reservoir at temperature `T_(1)` . It takes `200 J` of heat from the hot reservoir and delivers `120 J` of heat to the cold reservoir in a cycle. What could be the minimum temperature of hot reservoir?

Text Solution

Verified by Experts

The work done by the engine in a cycle is
`W=200 J-120 J=80 J`.
the efficiency of the engine is
`eta =(W)/(Q)=(80 J)/(200 J)=0.40`.
From carnot's theorem, no engine can have an efficiency greater than that of a carnot engine.
Thus, `0.40le 1 -T_(2)/T_1=(1)-(300 K)/(T_(1)`
or, `(300 K)/(T_(1)le 1-0.40=0.60`
or,`T_(1)ge(300 K)/(0.60)`
or, `T_(1)ge500 K`.
The minimum tempreture of the hot reservoir has to be 500 K.
Promotional Banner

Similar Questions

Explore conceptually related problems

A heat engine operates between a cold reservoir at temperature T_2=300K and a hot reservoir at temperature T_1 . It takes 200 J of heat from the hot reservoir and delivers 120 J of heat from the hot reservoir and delivers 120 J of heat to the cold reservoir in a cycle. What could be the minimum temperature of the hot reservoir?

An ideal Carnot heat engine with an efficiency of 30% . It absorbs heat from a hot reservoir at 727^(@)C . The temperature of the cold reservoir is

A carnot engine opeates between two reservoirs of temperature 900K and 300K. The engine performs 1200J of work per cycle. The heat energy in (J) delivered by the engine to the low temperature reservoir in a cycle is

Two ideal Carnot engines opeate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures T_(1) and T_(2) . The temperature of the hot reservoir of the first engine is T_(1) and the temperature of the cold reservoir of the second engine is T_(2) . T is the temperature of the sink of first engine which isi also the source for the second engine. How is T related to T_(1) and T_(2) if both the engines perform equal amount of work?

What will be the increment in heat energy radiated when the temperature of hot body is raised by 5% ?

A Carnot engine takes 3xx10^6 cal of heat from a reservoir at 627^@C and gives it to a sink at 27^@C . The work done by the engine is:

One end of rod of length L and cross-sectional area A is kept in a furance of temperature T_(1) . The other end of the rod is kept at at temperature T_(2) . The thermal conductivity of the material of the rod is K and emissivity of the rod is e . It is given that T_(2)=T_(S)+DeltaT where DeltaT lt lt T_(S) , T_(S) being the temperature of the surroundings. If DeltaT prop (T_(1)-T_(S)) , find the proportionality constant. Consider that heat is lost only by radiation at the end where the temperature of the rod is T_(2) .

The efficiency of a heat engine is defined as the ratio of the mechanical work done by the engine in one cycle to the heat absorbed from the high temperature source . eta = (W)/(Q_(1)) = (Q_(1) - Q_(2))/(Q_(1)) Cornot devised an ideal engine which is based on a reversible cycle of four operations in succession: isothermal expansion , adiabatic expansion. isothermal compression and adiabatic compression. For carnot cycle (Q_(1))/(T_(1)) = (Q_(2))/(T_(2)) . Thus eta = (Q_(1) - Q_(2))/(Q_(1)) = (T_(1) - T_(2))/(T_(1)) According to carnot theorem "No irreversible engine can have efficiency greater than carnot reversible engine working between same hot and cold reservoirs". A carnot engine whose low temperature reservoir is at 7^(@)C has an efficiency of 50% . It is desired to increase the efficiency to 70% . By how many degrees should the temperature of the high temperature reservoir be increased?

A calorimeter of heat capacity 100 J//K is at room temperature of 30^(@)C . 100g of water at 40^(@)C of specific heat 4200 J//kg-K is poured into the calorimeter. What is the temperature of water is calorimeter?

A cylindrical block of length 0.4 m and area of cross-section 0.04 m^2 is placed coaxially on a thin metal disc of mass 0.4 kg and of the same cross - section. The upper face of the cylinder is maintained at a constant temperature of 400 K and the initial temperature of the disc is 300K . if the thermal conductivity of the material of the cylinder is 10 "watt"// m.K and the specific heat of the material of the disc is 600J//kg.K , how long will it take for the temperature of the disc to increase to 350 K ? Assume for purpose of calculation the thermal conductivity of the disc to be very high and the system to be thermally insulated except for the upper face of the cylinder.