Question:easy
An ideal rigid diatomic gas \((γ = \frac{7}{5})\) undergoes an adiabatic change . If the relation between temperature and volume is \(TV^x =\) constant then the value of x is
An ideal rigid diatomic gas \((γ = \frac{7}{5})\) undergoes an adiabatic change . If the relation between temperature and volume is \(TV^x =\) constant then the value of x is
Show Hint
x equals gamma minus 1.
Updated On: Oct 1, 2026
- \(0.25\)
- \(0.30\)
- \(0.40\)
- \(0.60\)
Show Solution
The Correct Option is C
Solution and Explanation
Step 1: Derivation:
Substitute $P = \frac{nRT}{V}$ into $PV^\gamma = C$: $nRT\,V^{\gamma-1} = C$. Since $nR$ is constant, $TV^{\gamma-1}$ is constant.
Step 2: Insert gamma:
$\gamma = \frac{C_p}{C_v} = \frac{7/2R}{5/2R} = \frac75$.
Step 3: Answer:
$x = 0.4$.
Final Answer:
x equals 0.4, option (C). \[ \boxed{0.40} \]
Substitute $P = \frac{nRT}{V}$ into $PV^\gamma = C$: $nRT\,V^{\gamma-1} = C$. Since $nR$ is constant, $TV^{\gamma-1}$ is constant.
Step 2: Insert gamma:
$\gamma = \frac{C_p}{C_v} = \frac{7/2R}{5/2R} = \frac75$.
Step 3: Answer:
$x = 0.4$.
Final Answer:
x equals 0.4, option (C). \[ \boxed{0.40} \]
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