Question:
When a diatomic gas (rigid) undergoes adiabatic change, its pressure \((\mathrm{P})\) and temperature \((\mathrm{T})\) are related as \(P \propto T^c\). The value of \(c\) is
When a diatomic gas (rigid) undergoes adiabatic change, its pressure \((\mathrm{P})\) and temperature \((\mathrm{T})\) are related as \(P \propto T^c\). The value of \(c\) is
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For an adiabatic process P is proportional to T raised to gamma over gamma minus one.
Updated On: Nov 13, 2026
- 2.5
- 3.5
- 1.5
- 5.2
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
For an adiabatic process \(PV^{\gamma}=\text{constant}\) and \(PV=nRT\), giving \(P^{1-\gamma}T^{\gamma}=\text{constant}\), so \(P\propto T^{\gamma/(\gamma-1)}\).
Step 2: Value of gamma
A rigid diatomic gas has \(\gamma=\dfrac{7}{5}\).
Step 3: Calculation
\(c=\dfrac{\gamma}{\gamma-1}=\dfrac{7/5}{2/5}=\dfrac{7}{2}=3.5\)
Final Answer:
The value of c is 3.5. \[ \boxed{\text{(B) }3.5} \]
For an adiabatic process \(PV^{\gamma}=\text{constant}\) and \(PV=nRT\), giving \(P^{1-\gamma}T^{\gamma}=\text{constant}\), so \(P\propto T^{\gamma/(\gamma-1)}\).
Step 2: Value of gamma
A rigid diatomic gas has \(\gamma=\dfrac{7}{5}\).
Step 3: Calculation
\(c=\dfrac{\gamma}{\gamma-1}=\dfrac{7/5}{2/5}=\dfrac{7}{2}=3.5\)
Final Answer:
The value of c is 3.5. \[ \boxed{\text{(B) }3.5} \]
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