Vessels `1` and `2` contain `v = 1.2` moles of gaseous helium. The ratio of the vessels' volumes `V_2//V_1 = alpha = 2.0`, and the ratio of the absolute temperatures of helium in them `T_1//T_2 = beta = 1.5`. Assuming the gas be to ideal, find the difference of gas entropies in these vessels, `S_2 - S_1`.

Explanation

To calculate the required entropy difference we only have to calculate the entropy difference for a process in which the state of the gas in vessel `1` is changed to that in vessel `2`
`Delta S = v (int_(T_1)^((T_1)/(alpha beta)) C_V (dT)/(T) + int _((T_1)/(alpha beta))^((T_1)/(beta)) C_p (dT)/(T))`
=`v(C_p 1n alpha - C_V 1n alpha beta)`
=`v(R 1n alpha - (R)/(gamma - 1) 1n beta) = vR (1n alpha -(1n beta)/(gamma -1))`
With `gamma = (5)/(3), alpha = 2` and `beta = 1.5, v = 1.2`,
this gives `Delta S = 0.85 "Joule"//.^@K`.
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