Pressure and volume of an ideal gas are related as mathrm{PV}^{3 / 2}=mathrm{K} (Constant). work don

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11.Thermodynamics

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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 :

A

$2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right)$

B

$2\left(\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1\right)$

C

$2\left(\sqrt{\mathrm{P}_1} V_1-\sqrt{\mathrm{P}_2} V_2\right)$

D

$2\left(\mathrm{P}_2 \sqrt{\mathrm{V}_2}-\mathrm{P}_1 \sqrt{\mathrm{V}_1}\right)$

(JEE MAIN-2024)

Solution

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

Standard 11

Physics

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