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 :
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 :
- [JEE MAIN 2024]
- 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
$2\left(\mathrm{P}_2 \sqrt{\mathrm{V}_2}-\mathrm{P}_1 \sqrt{\mathrm{V}_1}\right)$
Similar Questions
A gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is
A gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is
Jet aircrafts fly at altitudes above $30000 \,ft$, where the air is very cold at $-40^{\circ} C$ and the pressure is $0.28 \,atm$. The cabin is maintained at $1 \,atm$ pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of $25^{\circ} C$, we will require in addition
Jet aircrafts fly at altitudes above $30000 \,ft$, where the air is very cold at $-40^{\circ} C$ and the pressure is $0.28 \,atm$. The cabin is maintained at $1 \,atm$ pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of $25^{\circ} C$, we will require in addition
- [KVPY 2011]
An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas?
An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas?
- [AIPMT 2015]
A sample of gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is : $(\mu=1 \mathrm{~mole})$
A sample of gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is : $(\mu=1 \mathrm{~mole})$
- [JEE MAIN 2024]
The volume of $1\; mole$ of an ideal gas with the adiabatic exponent $\gamma$ is changed according to the relation $V=\frac bT$ where $b =$ constant. The amount of heat absorbed by the gas in the process if the temperature is increased by $\triangle T$ will be
The volume of $1\; mole$ of an ideal gas with the adiabatic exponent $\gamma$ is changed according to the relation $V=\frac bT$ where $b =$ constant. The amount of heat absorbed by the gas in the process if the temperature is increased by $\triangle T$ will be
- [NEET 2017]