Home
Class 11
PHYSICS
Three moles of an ideal gas (Cp=7/2R) at...

Three moles of an ideal gas `(C_p=7/2R)` at pressure, `P_A` and temperature `T_A` is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure `P_A`.
(a) Sketch P-V and P-T diagrams for the complete process.
(b) Calculate the net work done by the gas, and net heat supplied to the gas during the complete process.

Text Solution

Verified by Experts

Diagrams of P-V and P-I are shown in Fig. (a) and (b)
The initial state of isothermal expansion is represented by A where pressure is `P_(A)` and volume `V_(A)`. Let the final state be represented by B where volume `V_(B)` is twice of `V_(A)`. Let the pressure be `P_(B)`. Then
`P_(A) V_(A) = P_(B) V_(B) = P_(B) (2V_(A))`
or `P_(B) = P_(A) (V_(A)//2V_(A)) = P_(A)//2`
When the molecule is compressed to initial volume, the process is represented by BC. Finally, the gas is compressed at constant volume to its original pressure. The process is shown by curve CA.
Similarly P-T diagram can be drawn
b. Wor in the process AB is given by
`W_(1) = nRT 1n (V_(B) - V_(A))`
`= 3 xx 8.314 xx T_(A) xx 1n 2`
`= 3 xx 8.314 xx T_(A) xx 0.693 = 17.29 T_(A)`
Work done in the process BC is given by
`W_(2) = P Delta V = P_(B) xx (V_(C ) - V_(B))`
`= ((P_(A))/(2)) xx (V_(A) - 2V_(A))`
`= - P_(A) V_(A)//2 = - nRT_(A)//2`
`= - 3RT_(A)//2 = - 3 xx 8.314 T_(A)//2 = - 12.471 T_(A)`
Work done doing process `C_(A)` is given by
`W_(3) = P Delta V = 0`
Net work `W = W_(1) + W_(2) + W_(3)`
` = 17.26 T_(A) - 12.45 T_(A) = 4.81 T_(A)`
As initial and final states of the gas are same
`Delta U = U_(A) = U_(A) = 0`
From the first law of thermodynaimcs
`Delta Q = Delta U + DeltaW = 0 + Delta W`
`Q = W` joules
Promotional Banner

Topper's Solved these Questions

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS|Exercise Exercise 2.1|20 Videos
  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS|Exercise Exercise 2.2|28 Videos
  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS|Exercise Interger|11 Videos
  • KINETIC THEORY OF GASES

    CENGAGE PHYSICS|Exercise Compression|2 Videos
  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS|Exercise Multiple Correct Answer Type|9 Videos

Similar Questions

Explore conceptually related problems

Three moles of an ideal gas (C_p=7/2R) at pressure p_0 and temperature T_0 is isothermally expanded to twice its initial volume. It is then compressed at a constant pressure to its original volume. (a) Sketch p-V and p-T diagram for complete process. (b) Calculate net work done by the gas. (c) Calculate net heat supplied to the gas during complete process. (Write your answer in terms of gas constant =R)

A sample of an ideal gas has pressure p_(0) , volume V_(0) and tempreture T_(0) . It is isothermally expanded to twice its oringinal volume.it is then compressed at constant pressure to have the original volume V_(0) . Finally, the gas is heated at constant volume to get the original tempreture.(a) show the process in a V-T diagram (b) calculate the heat absorbed in the process.

An ideal gas intially has pressure P volume V and temperature T . Its is isothermally expanded to four times of its original volume, then it is compressed at constant pressure to attain its original volume V . Finally, the gas is heated at constant volume to get the original temperature T . (a) Draw V-T curve (b) Calculate the total work done by the gas in the process.(given ln2 = 0.693)

If a gas is heated at constant pressure, its isothermal compressibility

One mole of an ideal gas at pressure P_(0) and temperature T_(0) is expanded isothermally to twice ist volume and then compressed at constant pressure to (V_(0) // 2) and the gas is brought bac to original state by a process in which P alpha V (pressure is direclty proportional to volume). The correct temperature of the process is

A gas is suddenly compressed to one fourth of its original volume. What will be its final pressure, if its initial pressure is p

A mass of ideal gas at pressure P is expanded isothermally to four times the original volume and then slowly compressed adiabatically to its original volume. Assuming gamma to be 1.5, the new pressure of the gas is

One gram mole of an ideal gas at N.T.P is first expanded isothermally to twice the origional volume. It is then compressed at constant volume, till its pressure is raised to the original value. Calculate the total amount of work done. Given R= 8.3 mol e^(_1)K^(-1) .