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QPages 77-80: Q10: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q10 Solution: An ideal gas ) is taken through a process in which the pressure …

An ideal gas Cp/Cv=γC_p/ C_v = \gamma) is taken through a process in which the pressure and the volume vary as p=aVbp = aV^b. Find the value of b for which the specific heat capacity in the process is zero.

Step-by-Step Verified Solution

**Answer:** b=−γb = -\gamma. **Step-by-Step Explanation:** For specific heat capacity to be zero, the process must be adiabatic: PVγ=constantPV^\gamma = \text{constant}. Given P=aVbP = aV^b, comparing with PVγ=constantPV^\gamma = \text{constant}: P∝V−γP \propto V^{-\gamma}, so b=−γb = -\gamma [citation:12].

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