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Thermodynamic processes

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Question

One mole of an ideal monatomic gas undergoes the process $P = α T^{1 / 2}$ , where $α$ is constant. If molar heat capacity of the gas is $β$ R when R = gas constant, then the value of $β$ is ___________

Moderate

Solution

$\begin{array}{l} P \propto T^{1 / 2} and P V = n R T \Rightarrow P V^{- 1} = constant \\ ∴ C = C_{V} + \frac{R}{1 - (- 1)} = \frac{3 R}{2} + \frac{R}{2} = 2 R \end{array}$

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Similar Questions

An ideal gas undergoes a process in which $P V^{- a} =$ constant, where $V$ is the volume occupied by the gas initially at pressure $P$ . At the end of the process, rms speed of gas molecules has become $a^{1 / 2}$ times of its initial value. What will be the value of $C_{V}$ so that energy transferred by the heat to the gas is $' a'$ times of the initial energy $(Δ Q = a P V)$

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