The pressure and volume of an ideal gas are related as (Constant). The work done when the gas is taken from state to state is

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Q.
The pressure and volume of an ideal gas are related as $P V^{3 / 2} = K$ (Constant). The work done when the gas is taken from state $A (P_{1}, V_{1}, T_{1})$ to state $B (P_{2}, V_{2}, T_{2})$ is [2024]

1 $2 (P_{1} V_{1} - P_{2} V_{2})$

2 $2 (P_{2} V_{2} - P_{1} V_{1})$

3 $2 (\sqrt{P_{1}} V_{1} - \sqrt{P_{2}} V_{2})$

4 $2 (P_{2} \sqrt{V_{2}} - P_{1} \sqrt{V_{1}})$

Ans.
(1)

For $P V^{x} =$ constant

$W = \frac{n R ∆ T}{1 - x}$

Here $x = \frac{3}{2}$

$∴$ $W = \frac{P_{2} V_{2} - P_{1} V_{1}}{- \frac{1}{2}}$

$= 2 (P_{1} V_{1} - P_{2} V_{2})$

Solution

Q.
The pressure and volume of an ideal gas are related as $P V^{3 / 2} = K$ (Constant). The work done when the gas is taken from state $A (P_{1}, V_{1}, T_{1})$ to state $B (P_{2}, V_{2}, T_{2})$ is [2024]

1 $2 (P_{1} V_{1} - P_{2} V_{2})$

2 $2 (P_{2} V_{2} - P_{1} V_{1})$

3 $2 (\sqrt{P_{1}} V_{1} - \sqrt{P_{2}} V_{2})$

4 $2 (P_{2} \sqrt{V_{2}} - P_{1} \sqrt{V_{1}})$

Ans.
(1)

For $P V^{x} =$ constant

$W = \frac{n R ∆ T}{1 - x}$

Here $x = \frac{3}{2}$

$∴$ $W = \frac{P_{2} V_{2} - P_{1} V_{1}}{- \frac{1}{2}}$

$= 2 (P_{1} V_{1} - P_{2} V_{2})$

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Solution

Q. The pressure and volume of an ideal gas are related as PV3/2=K (Constant). The work done when the gas is taken from state A(P1,V1,T1) to state B(P2,V2,T2) is [2024]

1 2(P1V1-P2V2)

2 2(P2V2-P1V1)

3 2(P1V1-P2V2)

4 2(P2V2-P1V1)

Ans. (1) For PVx= constant W=nR∆T1-x Here x=32 ∴ W=P2V2-P1V1-12 =2(P1V1-P2V2)

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Q.
The pressure and volume of an ideal gas are related as $P V^{3 / 2} = K$ (Constant). The work done when the gas is taken from state $A (P_{1}, V_{1}, T_{1})$ to state $B (P_{2}, V_{2}, T_{2})$ is [2024]

1 $2 (P_{1} V_{1} - P_{2} V_{2})$

2 $2 (P_{2} V_{2} - P_{1} V_{1})$

3 $2 (\sqrt{P_{1}} V_{1} - \sqrt{P_{2}} V_{2})$

4 $2 (P_{2} \sqrt{V_{2}} - P_{1} \sqrt{V_{1}})$

Ans.
(1)

For $P V^{x} =$ constant

$W = \frac{n R ∆ T}{1 - x}$

Here $x = \frac{3}{2}$

$∴$ $W = \frac{P_{2} V_{2} - P_{1} V_{1}}{- \frac{1}{2}}$

$= 2 (P_{1} V_{1} - P_{2} V_{2})$