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 |
- A$(A) \rightarrow q, (B) \rightarrow p \& r, (C) \rightarrow p \& s, (D) \rightarrow q \& s$
- B$(A) \rightarrow p, (B) \rightarrow s \& r, (C) \rightarrow p \& q, (D) \rightarrow q \& r$
- C$(A) \rightarrow p, (B) \rightarrow p \& s, (C) \rightarrow p \& s, (D) \rightarrow q \& p$
- D$(A) \rightarrow r, (B) \rightarrow p \& r, (C) \rightarrow s \& s, (D) \rightarrow r \& s$
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Similar Questions
In the $p-V$ diagram below,the dashed curved line is an adiabat. For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabat (solid line in the diagram),heat is (Hint: consider the variation in temperature from $X$ to $Y$ along the straight line)
$A$ gas is governed by an equation $V = \frac{aT^3}{P}$,where $P, V$,and $T$ are pressure,volume,and temperature of the gas respectively,and $a$ is a constant. If the temperature of the gas is doubled at constant pressure,then the work done by the gas is: (in $aT^3$)
Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.
Process Condition $(I)$ Adiabatic $(A) \Delta W = 0$ $(II)$ Isothermal $(B) \Delta Q = 0$ $(III)$ Isochoric $(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$ $(IV)$ Isobaric $(D) \Delta U = 0$
| Process | Condition |
| $(I)$ Adiabatic | $(A) \Delta W = 0$ |
| $(II)$ Isothermal | $(B) \Delta Q = 0$ |
| $(III)$ Isochoric | $(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$ |
| $(IV)$ Isobaric | $(D) \Delta U = 0$ |
One mole of an ideal gas is taken through a cyclic process with alternating isothermal and adiabatic curves. In the $P-V$ diagram, $AB, CD, EF$ are isothermal curves at absolute temperatures $T_1, T_2,$ and $T_3$ respectively, and $BC, DE,$ and $FA$ are adiabatic curves. If $\frac{V_B}{V_A} = 2$ and $\frac{V_D}{V_C} = 2$, then for the cycle shown in the figure, four statements are made below. (Figure is not drawn to scale)
Statement $1$: Ratio of volumes $\frac{V_E}{V_F} = 4$
Statement $2$: Magnitude of work done in isothermal compression $EF$ is $2RT_3 \ln(2)$
Statement $3$: Ratio of heat supplied to the gas in process $AB$ to heat rejected by the gas in process $EF$ is $\frac{T_1}{T_3}$
Statement $4$: Net work done by the gas in the cycle $ABCDEFA$ is $(T_1 + T_2 - 2T_3) R \ln(2)$
Find the number of correct statements given for the cyclic process followed by the gas.
Statement $1$: Ratio of volumes $\frac{V_E}{V_F} = 4$
Statement $2$: Magnitude of work done in isothermal compression $EF$ is $2RT_3 \ln(2)$
Statement $3$: Ratio of heat supplied to the gas in process $AB$ to heat rejected by the gas in process $EF$ is $\frac{T_1}{T_3}$
Statement $4$: Net work done by the gas in the cycle $ABCDEFA$ is $(T_1 + T_2 - 2T_3) R \ln(2)$
Find the number of correct statements given for the cyclic process followed by the gas.
The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA$. The part $ABC$ is a semi-circle and $CDA$ is half of an ellipse. Then,
$(A)$ the process during the path $A \rightarrow B$ is isothermal
$(B)$ heat flows out of the gas during the path $B \rightarrow C \rightarrow D$
$(C)$ work done during the path $A \rightarrow B \rightarrow C$ is zero
$(D)$ positive work is done by the gas in the cycle $ABCDA$
$(A)$ the process during the path $A \rightarrow B$ is isothermal
$(B)$ heat flows out of the gas during the path $B \rightarrow C \rightarrow D$
$(C)$ work done during the path $A \rightarrow B \rightarrow C$ is zero
$(D)$ positive work is done by the gas in the cycle $ABCDA$
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