The coefficient of isothermal elasticity $E_{\theta}$ and the coefficient of adiabatic elasticity $E_{\phi}$ are related by $(\gamma = C_p/C_v)$.
- A$E_{\theta} = \gamma E_{\phi}$
- B$E_{\phi} = \gamma E_{\theta}$
- C$E_{\theta} = \gamma / E_{\phi}$
- D$E_{\theta} = \gamma^2 E_{\phi}$
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Similar Questions
In Column $-I$ processes and in Column $-II$ formulas of work are given. Match them appropriately:
Column $-I$ Column $-II$ $(a)$ Isothermal process $(i)$ $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$ $(b)$ Adiabatic process $(ii)$ $W = P\Delta V$ $(iii)$ $W = 2.303\mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$
| Column $-I$ | Column $-II$ |
|---|---|
| $(a)$ Isothermal process | $(i)$ $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$ |
| $(b)$ Adiabatic process | $(ii)$ $W = P\Delta V$ |
| $(iii)$ $W = 2.303\mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$ |
Easy
View SolutionMatch the following:
Column $I$ Column $II$ $A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process $1$. $\frac{T_1}{T_1-T_2}$ $B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process $2$. $\frac{T_2}{T_1-T_2}$ $C$. Coefficient of performance of a refrigerator $3$. $\frac{\gamma}{\gamma-1}$ $D$. Coefficient of performance of a heat pump $4$. $\gamma$
Codes:
$A \quad B \quad C \quad D$
| Column $I$ | Column $II$ |
| $A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process | $1$. $\frac{T_1}{T_1-T_2}$ |
| $B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process | $2$. $\frac{T_2}{T_1-T_2}$ |
| $C$. Coefficient of performance of a refrigerator | $3$. $\frac{\gamma}{\gamma-1}$ |
| $D$. Coefficient of performance of a heat pump | $4$. $\gamma$ |
Codes:
$A \quad B \quad C \quad D$
$A$ monatomic gas at a pressure $P$, having a volume $V$, expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (Take $\gamma = 5/3$)
MediumAIPMT 2014
View SolutionIn Column-$I$ processes and in Column-$II$ the first law of thermodynamics are given. Match them appropriately:
Column-$I$ Column-$II$ $(a)$ Adiabatic $(i)$ $\Delta Q = \Delta U$ $(b)$ Isothermal $(ii)$ $\Delta Q = \Delta W$ $(iii)$ $\Delta U = -\Delta W$
| Column-$I$ | Column-$II$ |
|---|---|
| $(a)$ Adiabatic | $(i)$ $\Delta Q = \Delta U$ |
| $(b)$ Isothermal | $(ii)$ $\Delta Q = \Delta W$ |
| $(iii)$ $\Delta U = -\Delta W$ |
Easy
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 |
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