The pressure and volume of an ideal gas are related as PV^32=K (Constant). The work done when the gas is taken from state AP_1, V_1, T_1 to state BP_2, V_2, T_2 is :

Correct answer: (A) 2(P_1V_1-P_2V_2). For PV^x= constant, work done by the gas is given by, W=(nRΔT)/(1−x)=(P_2V_2-P_1V_1)/(1−x). Here x=3/2, therefore we can write ∴W=(P_2V_2−P_1V_1)/(−12) =2P_1V_1−P_2V_2

Q72 / 90 · JEE Main 2024 (01 Feb Shift 1) · Physics

The pressure and volume of an ideal gas are related as $P V^{\frac{3}{2}} = K$ (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 :

Correct answer
A
$2 (P_{1} V_{1} - P_{2} V_{2})$
B
$2 (P_{2} V_{2} - P_{1} V_{1})$
C
$2 (\sqrt{P_{1}} V_{1} - \sqrt{P_{2}} V_{2})$
D
$2 (P_{2} \sqrt{V_{2}} - P_{1} \sqrt{V_{1}})$

Solution

For $P V^{x} =$ constant, work done by the gas is given by,

$W = \frac{n R Δ T}{1 - x} = \frac{P_{2} V_{2} - P_{1} V_{1}}{1 - x}$ .

Here $x = \frac{3}{2}$ , therefore we can write

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

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

Hence, the correct answer is option: 'A'.

Relevant Questions

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure kPa and temperature K. K06 Apr, 2026 (M)Thermodynamic Processes
A certain gas is isothermally compressed to of its initial volume ( litre) by applying required pressure. If the bulk modulus of the gas is 06 Apr, 2026 (M)Thermodynamic Processes
A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is06 Apr, 2026 (E)Thermodynamic Processes
An ideal gas at pressure and temperature is expanding such that constant. The coefficient of volume expansion of the gas is _______.05 Apr, 2026 (E)Thermodynamic Processes
An ideal gas undergoes a process maintaining relation between pressure and volume as , where and are constants. If two samples and (two mole04 Apr, 2026 (M)Thermodynamic Processes
A vessel contains m of a gas at pressure bar and temperature C with and . It is expanded adiabatically till pressure falls to bar. The work 02 Apr, 2026 (M)Thermodynamic Processes

The pressure and volume of an ideal gas are related as PV32=K (Constant). The work done when the gas is taken from state AP1, V1, T1 to state BP2, V2, T2 is :

Solution

Relevant Questions

The pressure and volume of an ideal gas are related as $P V^{\frac{3}{2}} = K$ (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 :