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.

Given γ = 1.5 T=300 K, initial volume V1=1 L, Final volume V2=1/2 L. Let P1 and P2 be the initial and final pressures

(a)Here the process is adiabatic since volume is changed suddenly,

i.e.

(b)P1=100 KPa =10^{5} Pa ,P2=2^{1.5}(10^{5}) KPa

Work done in adiabatic process,

(c) Here dQ=0, as it an adiabatic process

By first law of thermodynamics,

i.e.

(d)For an adiabatic process, let TI and T2 be initial and final temperature

TV^{γ -1}=constant

I.e.

(e)Here the pressure is kept constant, i.e. isobaric

Work done in an isobaric process ,

Here,

Work done,

(f)Here the process is isothermal.

Work done,

(g)Work done in the cycle,

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