In a certain polytropic process, the volume of argon was increased 4 times. Simultaneously, the pres

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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

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$PV^{x} = 	ext{Constant}$$\Rightarrow P_{1}V_{1}^{x} = P_{2}V_{2}^{x} \Rightarrow \frac{P_{1}}{P_{2}} = \left( \frac{V_{2}}{V_{1}} ight)^{x} \Rightarrow 8 = 4^{x} \Rightarrow x = \frac{3}{2} $$$	ext{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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