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An ideal gas is taken through a process ...

An ideal gas is taken through a process in which the process equation is given as `P=kV^(alpha)`, where k and `alpha` are positive constants. Find the value of `alpha` for which in this process molar heat capacity becomes zero.

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To solve the problem, we need to find the value of \( \alpha \) for which the molar heat capacity \( C \) of the ideal gas becomes zero during the process defined by the equation \( P = kV^{\alpha} \). ### Step-by-Step Solution: 1. **Understanding the Process:** The given process is defined by the equation \( P = kV^{\alpha} \). This is a form of a polytropic process where \( P \) is the pressure, \( V \) is the volume, and \( k \) and \( \alpha \) are constants. 2. **Relating Pressure and Volume:** ...
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