Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)
- A$25.2$
- B$35$
- C$42$
- D$70$
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Starting at temperature $300 \; K,$ one mole of an ideal diatomic gas $(\gamma=1.4)$ is first compressed adiabatically from volume $V_{1}$ to $V_{2}=\frac{V_{1}}{16}.$ It is then allowed to expand isobarically to volume $2V_{2}.$ If all the processes are quasi-static,then the final temperature of the gas (in $K$) is (to the nearest integer):
DifficultJEE MAIN 2020
View SolutionAn ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2V$, the final pressure is $P_a$. The ratio $\frac{P_a}{P_i}$ is
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View SolutionThree moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperatures in different states are: $T_1 = 400\, K, T_2 = 800\, K, T_3 = 2400\, K$ and $T_4 = 1200\, K.$ The work done by the gas during the cycle is ........ $kJ$.
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View SolutionColumn $I$ contains a list of processes involving the expansion of an ideal gas. Match this with Column $II$ describing the thermodynamic change during this process.
Column $I$ Column $II$ $(A)$ An insulated container has two chambers separated by a valve. Chamber $I$ contains an ideal gas and Chamber $II$ has a vacuum. The valve is opened. $(p)$ The temperature of the gas decreases $(B)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-2}$ $(q)$ The temperature of the gas increases or remains constant $(C)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-4/3}$ $(r)$ The gas loses heat $(D)$ An ideal monoatomic gas expands such that its pressure $P$ and volume $V$ follow the behavior shown in the graph $(s)$ The gas gains heat
| Column $I$ | Column $II$ |
| $(A)$ An insulated container has two chambers separated by a valve. Chamber $I$ contains an ideal gas and Chamber $II$ has a vacuum. The valve is opened. | $(p)$ The temperature of the gas decreases |
| $(B)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-2}$ | $(q)$ The temperature of the gas increases or remains constant |
| $(C)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-4/3}$ | $(r)$ The gas loses heat |
| $(D)$ An ideal monoatomic gas expands such that its pressure $P$ and volume $V$ follow the behavior shown in the graph | $(s)$ The gas gains heat |
Check if the following statements are true or false:
$1.$ For an adiabatic process,$T V^{\gamma - 1} = \text{constant}$.
$2.$ The charging process of a battery is a reversible process.
$3.$ Water falling from a height is a reversible process.
$4.$ Internal energy,volume,and mass are intensive variables,while pressure,temperature,and density are extensive variables.
$1.$ For an adiabatic process,$T V^{\gamma - 1} = \text{constant}$.
$2.$ The charging process of a battery is a reversible process.
$3.$ Water falling from a height is a reversible process.
$4.$ Internal energy,volume,and mass are intensive variables,while pressure,temperature,and density are extensive variables.
Medium
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