Starting with the same initial conditions,an ideal gas expands from volume $V_{i}$ to $V_{f}$ in three different ways. The work done by the gas is $W_{1}$ if the process is purely isothermal,$W_{2}$ if the process is purely adiabatic,and $W_{3}$ if the process is purely isobaric. Then,choose the correct option.
- A$W_{1} < W_{2} < W_{3}$
- B$W_{2} < W_{3} < W_{1}$
- C$W_{3} < W_{1} < W_{2}$
- D$W_{2} < W_{1} < W_{3}$
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Column $I$ 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 |
The $P-V$ diagram shown represents the thermodynamic cycle of an engine operating with an ideal monatomic gas. The amount of heat extracted from the source in a single cycle is:
If one mole of an ideal gas goes through the process $A \rightarrow B$ and $B \rightarrow C$ as shown in the $P-V$ diagram. Given that $T_A = 400 \, K$ and $T_C = 400 \, K$. If $\frac{P_B}{P_A} = \frac{1}{5}$,then find the total heat supplied to the gas (in $J$). (in $.2$)
MediumAIIMS 2019
View Solution$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas
$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)
DifficultAP EAMCET 2010
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