Question
Two moles of an ideal gas (Cv,m = 1.5R) is subjected to the following changes in states.
$A\left( \text{500 K, 5 bar} \right)\overset{\quad\text{Reversible }\text{isothermalExpansion}\quad}{\rightarrow}B\overset{\quad\text{Isochoric cooling}\quad}{\rightarrow}C\left( \text{250 K, 1 bar} \right)\overset{\quad\text{Single stage }\text{adiabaticcompression}\quad}{\rightarrow}D\left( \text{3 bar} \right)$
The correct statement(s) is/are
Options
Solution
Process BC: $\frac{P_{B}}{T_{B}} = \frac{P_{C}}{T_{C}} \Rightarrow \frac{P_{B}}{500} = \frac{1}{250} \Rightarrow P_{B} = 2\text{ bar}$
and $\Delta U_{BC} = n.C_{V,m}\left( T_{C} - T_{B} \right) = 2 \times 1.5R \times (250 - 500) = - 750\text{ R}$
Process CD: $\Delta U = w \Rightarrow n.C_{V,m}\left( T_{D} - T_{C} \right) = - P_{\text{ext}}\left( V_{D} - V_{C} \right)$
Or, $n \times 1.5R \times \left( T_{D} - T_{C} \right) = - P_{D}\left( \frac{nRT_{D}}{P_{D}} - \frac{nRT_{C}}{P_{C}} \right) \Rightarrow T_{D} = 450\text{ K}$
and $\Delta H_{CD} = n.C_{P,m}.\left( T_{D} - T_{C} \right) = 2 \times 2.5R \times (450 - 250) = 1000\text{ R}$
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