First slide

Thermodynamic processes

Question

During an adiabatic process, the pressure of a gas found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_{P}}{C_{V}}$ for the gas is__________

Moderate

Solution

given $P α T^{3}$
$\begin{array}{l} P α T^{(\frac{y}{γ - 1})} \\ \frac{γ}{γ - 1} = 3 \\ γ = 3 γ - 3 \\ γ = \frac{3}{2} \end{array}$

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