A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $\mathrm{P}…

A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $\mathrm{P} \alpha \mathrm{T}^{\mathrm{x}}$ where the value of x is
  1. $3.5$
  2. $2.5$
  3. $4.5$
  4. 3

Solution

For an adiabatic process, $\mathrm{TP}^{\frac{1-\gamma}{\gamma}}=\text { constant }...(i)$
For diatomic gas, $\begin{array}{ll} & \gamma=\frac{7}{5} \\ \therefore \quad & \frac{1-\gamma}{\gamma}=-\frac{2}{7} \\ & \mathrm{TP}^{-2 / 7}=\text { constant } \\ & \Rightarrow \mathrm{P} \propto \mathrm{~T}^{7 / 2} \Rightarrow \mathrm{P} \propto \mathrm{~T}^{3.5} \\ \therefore \quad & x=3.5 \end{array}$ .

Asked in: MHT CET 2024 (03 May Shift 2)

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