Q22 of 27 Page 87

The initial state of a certain gas is (Pi, Vi ,Ti ). It undergoes expansion till its volume becomes Vf. Consider the following two cases:

(a) the expansion takes place at constant temperature.


(b) the expansion takes place at constant pressure. Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas more?


P vs. V for isothermal process is like hyperbola.


If initial and final conditions for an ideal gas is given and then for various processes the plot is given below




a. At constant temperature (isothermal process)



b. At constant pressure (isobaric process)



Work done is given by the area under the curve of the P Vs V plots given above.


Since area under the curve of the isobaric process is more than the isothermal process. Therefore, more work is done in isobaric process.


More from this chapter

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20

In a refrigerator one removes heat from a lower temperature and deposits to the surroundings at a higher temperature. In this process, mechanical work has to be done, which is provided by an electric motor. If the motor is of 1kW power, and heat is transferred from –3°C to 27°C, find the heat taken out of the refrigerator per second assuming its efficiency is 50% of a perfect engine.

 21

If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature (27 °C), find the temperature inside the refrigerator.

 23

Consider a P-V diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in Fig. 12.9.

(a) Find the work done when the gas is taken from state 1 to state 2.


(b) What is the ratio of temperature T1/T2, if V2 = 2V1?


(c) Given the internal energy for one mole of gas at temperature T is (3/2) RT, find the heat supplied to the gas when it is taken from state 1 to 2, with V2 = 2V1.



 24

A cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in Fig. 12.10.


A to B: volume constant


B to C: adiabatic


C to D: volume constant


D to A: adiabatic


Vc = VD = 2VA = 2VB


(a) In which part of the cycle heat is supplied to the engine from outside?


(b) In which part of the cycle heat is being given to the surrounding by the engine?


(c) What is the work done by the engine in one cycle? Write your answer in term of PA, PB, VA.


(d) What is the efficiency of the engine?


[ γ = for the gas], ( Cv = R for one mole)