JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2024
- Hard
- MCQ
The pressure and volume of an ideal gas are related as \(\mathrm{PV}^{3 / 2}=\mathrm{K}\) (Constant). The work done when the gas is taken from state \(A\left(P_1, V_1, T_1\right)\) to state \(\mathrm{B}\left(\mathrm{P}_2, \mathrm{~V}_2, \mathrm{~T}_2\right)\) is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right)\)
Step-by-step Solution
Detailed explanation
For \(\mathrm{PV}^{\mathrm{x}}=\) constant
If work done by gas is asked then
\({W}=\frac{\mathrm{nR} \Delta \mathrm{T}}{1-\mathrm{x}}\)
Here x \(=\frac{3}{2}\)
\( W =\frac{\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1}{-\frac{1}{2}}\)
\(=2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right) \ldots . \text { Option (1) is correct }\)
If work done by external is asked then
\(\mathrm{W}=-2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right) \ldots \ldots\) Option \((2)\) is correct
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