ThermodynamicsHard
Question
In a certain polytropic process, the volume of argon was increased 4 times. Simultaneously, the pressure decreased 8 times. The molar heat capacity of argon in this process, assuming the gas to be ideal, is
Options
A.−4.2 J/K-mol
B.+4.2 J/K-mol
C.12.47 J/K-mol
D.20.78 J/K-mol
Solution
$PV^{x} = \text{Constant}$
$\Rightarrow P_{1}V_{1}^{x} = P_{2}V_{2}^{x} \Rightarrow \frac{P_{1}}{P_{2}} = \left( \frac{V_{2}}{V_{1}} \right)^{x} \Rightarrow 8 = 4^{x} \Rightarrow x = \frac{3}{2} $$$\text{Now, }C_{m} = C_{V,m} + \frac{R}{1 - x} = \frac{3R}{2} + \frac{R}{1 - \frac{3}{2}} = - \frac{R}{2}$$
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