Q23 of 65 Page 77

Three samples A, B and C of the same gas (γ = 1.5) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressure is equal for the three samples, find the ratio of the initial pressures.

Let VA, VB, VC be the volume of three gases and TA, TB, TCbe the temperature of A, B, C gas


Given, TA=TB=TC, VA=VB=VC


Here A is undergoing an isothermal process, where V1= VA, V2=2VA


Let P1 and P2 be the initial and final pressures,


Then,





Here B is adiabatic,


PVγ = const, where V1= VB, V2=2VB


Let P1 and P2 be the initial and final pressures,


I.e.




Here C is isobaric ,the pressure remains constant and equal to


Now, as the final pressures are equal for all the gases



, ratio of the initial pressures


More from this chapter

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21

Consider a given sample of an ideal gas (CP/CV = γ) having initial pressure P0 and volume V0.

(a) The gas is isothermally taken to a pressure P0/2 and from there adiabatically to a pressure P0/4. Find the final volume.


(b) The gas is brought back to its initial state. It is adiabatically taken to a pressure P0/2 and from there isothermally to a pressure P0/4. Find the final volume.


 22

A sample of an ideal gas (γ = 1.5) is compressed adiabatically from a volume of 150 cm3 to 50 cm3. The initial pressure and the initial temperature are 150 kPa and 300 K. Find

(a) the number of moles of the gas in the sample,


(b) the molar heat capacity at constant volume,


(c) the final pressure and temperature,


(d) the work done by the gas in the process and


(e) the change in internal energy of the gas.


 24

Two samples A and B of the same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume. If the work done by the gas is the same for the two cases, show that γ satisfies the equation 1 – 21– γ = (γ – 1) ln2.

 25

1 litre of an ideal gas (γ = 1.5) at 300 K is suddenly compressed to half its original volume.

(a) Find the ratio of the final pressure to the initial pressure.


(b) If the original pressure is 100 kPa, find the work done by the gas in the process.


(c) What is the change in internal energy?


(d) What is the final temperature?


(e) The gas is now cooled to 300 K keeping its pressure constant.


Calculate the work done during the process.


(f) The gas is now expanded isothermally to achieve its original volume of 1 litre. Calculate the work done by the gas.


(g) Calculate the total work done in the cycle.