MHT CET · Physics · Thermodynamics
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
- A \(3.5\)
- B \(2.5\)
- C \(4.5\)
- D 3
Answer & Solution
Correct Answer
(A) \(3.5\)
Step-by-step Solution
Detailed explanation
For an adiabatic process,
\(\mathrm{TP}^{\frac{1-\gamma}{\gamma}}=\text { constant }...(i)\)
For diatomic gas,
\(\begin{array}{ll}
& \gamma=\frac{7}{5} \\
\therefore \quad & \frac{1-\gamma}{\gamma}=-\frac{2}{7} \\
& \mathrm{TP}^{-2 / 7}=\text { constant } \\
& \Rightarrow \mathrm{P} \propto \mathrm{~T}^{7 / 2} \Rightarrow \mathrm{P} \propto \mathrm{~T}^{3.5} \\
\therefore \quad & x=3.5
\end{array}\)
\(\mathrm{TP}^{\frac{1-\gamma}{\gamma}}=\text { constant }...(i)\)
For diatomic gas,
\(\begin{array}{ll}
& \gamma=\frac{7}{5} \\
\therefore \quad & \frac{1-\gamma}{\gamma}=-\frac{2}{7} \\
& \mathrm{TP}^{-2 / 7}=\text { constant } \\
& \Rightarrow \mathrm{P} \propto \mathrm{~T}^{7 / 2} \Rightarrow \mathrm{P} \propto \mathrm{~T}^{3.5} \\
\therefore \quad & x=3.5
\end{array}\)
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