One mole of an ideal gas is subjected to adiabatic expansion from initial state of (10 atm, 300 K) to final pressure of 1 atm against constant external pressure. Which of the following options contain correct change in thermodynamics parameters for the above process. (Given: $γ$ of gas $= \frac{4}{3}$ ).

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$Δ U = 270 R$

$Δ S = R \ln 10$

$Δ H = 230 R$

$w = - 202.5 R$

answer is D.

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Detailed Solution

Here, we have,

$\begin{array}{l} q = 0; Δ U = w; 1 \times C_{v} (T_{2} - T_{1}) \\ = - 1 \times (\frac{1 \times R \times T_{2}}{1} - \frac{1 \times R \times T_{1}}{10}) \\ \Rightarrow 3 \times (T_{2} - 300) = - (T_{2} - 30) \\ \Rightarrow T_{2} = 232.5 K \\ Δ H = 1 \times 4 R \times (300 - 232.5) = - 270 R \\ Δ U = 1 \times 3 R \times (300 - 232.5) = - 202.5 R = w \\ Δ S_{sys} = n C_{v} \ln (\frac{T_{2}}{T_{1}}) + n R \ln (\frac{V_{2}}{V_{1}}) \end{array}$