JEE Mains · Physics · STD 11 - 11. thermodynamics
A sample of \(1\) mole gas at temperature \(\mathrm{T}\) is adiabatically expanded to double its volume. If adiabatic constant for the gas is \(\gamma=\frac{3}{2}\), then the work done by the gas in the process is _______.
- A \(\mathrm{RT}[2-\sqrt{2}]\)
- B \(\frac{\mathrm{R}}{\mathrm{T}}[2-\sqrt{2}]\)
- C \(\mathrm{RT}[2+\sqrt{2}]\)
- D \(\frac{T}{R}[2+\sqrt{2}]\)
Answer & Solution
Correct Answer
(A) \(\mathrm{RT}[2-\sqrt{2}]\)
Step-by-step Solution
Detailed explanation
\(\mathrm{TV}^{\gamma-1}=\text { constant }\) \(\Rightarrow \mathrm{T}(\mathrm{V})^{\frac{3}{2}-1}=\mathrm{T}_{\mathrm{f}}(2 \mathrm{~V})^{\frac{3}{2}-1}\) \(\Rightarrow \mathrm{TV}^{\frac{1}{2}}=\mathrm{T}_{\mathrm{f}}(2)^{\frac{1}{2}}(\mathrm{~V})^{\frac{1}{2}}\)…
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