Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal diatomic gas at temperature $T$ $K$. The piston of cylinder $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in cylinder $B$ is (where $\gamma = \frac{C_{P}}{C_{V}}$):
- A$2 dT_{A}$
- B$\frac{dT_{A}}{2}$
- C$\gamma dT_{A}$
- D$\frac{dT_{A}}{\gamma}$
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An ideal gas at pressure $P$ and volume $V$ is expanded to volume $2V$. Column $I$ represents the thermodynamic processes used during expansion. Column $II$ represents the work done during these processes in random order:
Column $I$ Column $II$ $(p)$ isobaric $(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$ $(q)$ isothermal $(y)$ $PV$ $(r)$ adiabatic $(z)$ $PV \ln 2$
The correct matching of column $I$ and column $II$ is given by:
| Column $I$ | Column $II$ |
| $(p)$ isobaric | $(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$ |
| $(q)$ isothermal | $(y)$ $PV$ |
| $(r)$ adiabatic | $(z)$ $PV \ln 2$ |
The correct matching of column $I$ and column $II$ is given by:
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View Solution$A$ gas follows $VT^2 = \text{constant}$. The coefficient of volume expansion of the gas is
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View SolutionAn ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume ($\gamma = 1.4$ and $2^{-1.4} = 0.38$). The ratio of the final to initial pressure is (in $: 1$)
DifficultWBJEE 2011
View SolutionWhich of the following is an equivalent cyclic process corresponding to the thermodynamic cycle given in the figure? Where, $1 \rightarrow 2$ is adiabatic.
$A$ gas is expanded from an initial state to a final state along a path on a $P-V$ diagram. The path consists of $(i)$ an isothermal expansion of work $50 J$,$(ii)$ an adiabatic expansion,and $(iii)$ an isothermal expansion of work $20 J$. If the internal energy of the gas is changed by $-30 J$,then the work done by the gas during the adiabatic expansion is: (in $J$)
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