An ideal gas with specific heat ratio confined to a cylinder is put through a cl

Question

An ideal gas with specific heat ratio confined to a cylinder is put through a closed cycle. Initially, the gas is at Pi, Vi, and Ti. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume.

(b) Determine the volume (VC) at the end of the adiabatic expansion. (Use the following as necessary: and Vi.)

(c) Find the temperature (TB) of the gas at the start of the adiabatic expansion. (Use the following as necessary: , Ti, and Pi.)

(d) Find the temperature (TA) at the end of the cycle. (Use the following as necessary: , Ti, and Pi.)

(e) What was the net work done on the gas for this cycle? (Use the following as necessary: , Ti, Vi, and Pi.)

Explanation / Answer

a)    pressure at end of constant volume = 3Pi

=> (3Pi) * (Vi)   = (Pi) * (Vc)

=> Vc =   (3)1/ * Vi

b)    Here, Pi/Ti = 3Pi/TB

     => TB = 3 Ti

c)    temperature (TA) at the end of the cycle   = Ti

d)    net work done on the gas for this cycle =   PiVi(3 - (3)1/)/(-1) + Pi(Vi - (3)1/ * Vi)

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