The equation of state for a gas is given by $PV = nRT + \alpha V$, where $n$ is the number of moles and $\alpha $ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_o$ and $P_o$ respectively. The work done by the gas when its temperature doubles isobarically will be
The equation of state for a gas is given by $PV = nRT + \alpha V$, where $n$ is the number of moles and $\alpha $ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_o$ and $P_o$ respectively. The work done by the gas when its temperature doubles isobarically will be
- [JEE MAIN 2014]
- A
$\frac{{{P_0}{T_0}R}}{{{P_0} - \alpha }}$
- B
$\frac{{{P_0}{T_0}R}}{{{P_0} + \alpha }}$
- C
${P_0}{T_0}R\,\ln \,2$
- D
${{P_0}{T_0}R}$
Similar Questions
For adiabatic processes $\left( {\gamma = \frac{{{C_p}}}{{{C_v}}}} \right)$
For adiabatic processes $\left( {\gamma = \frac{{{C_p}}}{{{C_v}}}} \right)$
Which one is the correct option for the two different thermodynamic processes ?
Which one is the correct option for the two different thermodynamic processes ?
- [JEE MAIN 2021]
A gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$
A gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$
A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200\, {cm}^{3}$ to $300\, {cm}^{3}$. If the initial pressure is $200\, {kPa}$. The absolute value of the workdone by the gas in the process $= \,..... J.$
A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200\, {cm}^{3}$ to $300\, {cm}^{3}$. If the initial pressure is $200\, {kPa}$. The absolute value of the workdone by the gas in the process $= \,..... J.$
- [JEE MAIN 2021]
A certain amount of gas of volume $V$ at $27^{o}\,C$ temperature and pressure $2 \times 10^{7} \;Nm ^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$ )
A certain amount of gas of volume $V$ at $27^{o}\,C$ temperature and pressure $2 \times 10^{7} \;Nm ^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$ )
- [JEE MAIN 2022]