Following figure shows on adiabatic cylindrical container of volume ${V_0}$ divided by an adiabatic smooth piston (area of cross-section = $A$ ) in two equal parts. An ideal gas $({C_P}/{C_V} = \gamma )$ is at pressure $P_1$ and temperature $T_1$ in left part and gas at pressure $P_2$ and temperature $T_2$ in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose $ x$ = displacement of the piston)
Following figure shows on adiabatic cylindrical container of volume ${V_0}$ divided by an adiabatic smooth piston (area of cross-section = $A$ ) in two equal parts. An ideal gas $({C_P}/{C_V} = \gamma )$ is at pressure $P_1$ and temperature $T_1$ in left part and gas at pressure $P_2$ and temperature $T_2$ in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose $ x$ = displacement of the piston)
- A
${P_2}$
- B
${P_1}$
- C
$\frac{{{P_1}{{\left( {\frac{{{V_0}}}{2}} \right)}^\gamma }}}{{{{\left( {\frac{{{V_0}}}{2} + Ax} \right)}^\gamma }}}$
- D
$\frac{{{P_2}{{\left( {\frac{{{V_0}}}{2}} \right)}^\gamma }}}{{{{\left( {\frac{{{V_0}}}{2} + Ax} \right)}^\gamma }}}$
Similar Questions
Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, $1 \rightarrow 2$ is adiabatic.
(Graphs are schematic and are not to scale)
Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, $1 \rightarrow 2$ is adiabatic.
(Graphs are schematic and are not to scale)
- [JEE MAIN 2020]
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]
Given below are two statement
Statement $-I$ : What $\mu$ amount of an ideal gas undergoes adiabatic change from state $\left( P _{1}, V _{1}, T _{1}\right)$ to state $\left( P _{2}, V _{2}, T _{2}\right)$, the work done is $W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}$, where $\gamma=\frac{ C _{ P }}{ C _{ V }}$ and $R =$ universal gas constant,
Statement $-II$ : In the above case. when work is done on the gas. the temperature of the gas would rise.
Choose the correct answer from the options given below
Given below are two statement
Statement $-I$ : What $\mu$ amount of an ideal gas undergoes adiabatic change from state $\left( P _{1}, V _{1}, T _{1}\right)$ to state $\left( P _{2}, V _{2}, T _{2}\right)$, the work done is $W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}$, where $\gamma=\frac{ C _{ P }}{ C _{ V }}$ and $R =$ universal gas constant,
Statement $-II$ : In the above case. when work is done on the gas. the temperature of the gas would rise.
Choose the correct answer from the options given below
- [JEE MAIN 2022]
A gas ($\gamma = 1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10^5}\,N/{m^2}$. On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is
A gas ($\gamma = 1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10^5}\,N/{m^2}$. On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is
In adiabatic expansion
In adiabatic expansion