One mole of gas in a container is initially at a temperature 127C. It is expande

Question

One mole of gas in a container is initially at a temperature 127C. It is expanded adiabatically to twice its initial volume. Then, it is isothermally compressed to its original volume. The finaltemperature is found to be -3 C.What is gamma for the gas? [1.567] What change in its entropy has occurred ? [-5.8 J/K]

How do you work this out?
One mole of gas in a container is initially at a temperature 127C. It is expanded adiabatically to twice its initial volume. Then, it is isothermally compressed to its original volume. The finaltemperature is found to be -3 C.What is gamma for the gas? [1.567] What change in its entropy has occurred ? [-5.8 J/K]

How do you work this out?

Explanation / Answer

T1*V1^r-1 = T2*V2^r-1

T1 = 127+273.15 = 400.15

T2 = T

V1 = V

V2 = 2V

T1*V^(r-1) = T*(2V)^(r-1)


T1 = T*2^(r-1)

for isothermal process

T is constant and is given as = 3C i.e T = 273.15-3 = 270.15


400.15 = 270.15* 2^(r-1)

r-1 = ln_2*1.41121

r-1 = 0.567

r = 1.567









dS = -dQ/T = dW/T = 2.303*n*R*T(logV2/V1)/T

dS = -2.303*1*8.314*log(2/1)

dS = =5.8 J/K

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