Two moles of a triatomic gas $\left(\gamma = \frac{4}{3}\right)$ at temperature $327^{\circ} C$ expands adiabatically such that its volume becomes $8$ times its initial volume. Later,the temperature of the gas is doubled in an isochoric process. The total work done in the two processes is ($R$ - universal gas constant). (in $R$)
- A$900$
- B$1800$
- C$1200$
- D$300$
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$2$ moles of an ideal monoatomic gas is carried from a state $(p_{0}, V_{0})$ to state $(2 p_{0}, 2 V_{0})$ along a straight line path in a $p-V$ diagram. The amount of heat absorbed by the gas in the process is given by
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View Solution$N$ moles of an ideal diatomic gas are in a cylinder at temperature $T$. Suppose on supplying heat to the gas, its temperature remains constant but $n$ moles get dissociated into atoms. Heat supplied to the gas is
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View SolutionGiven below are two statements:
Statement $I:$ If heat is added to a system,its temperature must increase.
Statement $II:$ If positive work is done by a system in a thermodynamic process,its volume must increase.
In the light of the above statements,choose the correct answer from the options given below.
Statement $I:$ If heat is added to a system,its temperature must increase.
Statement $II:$ If positive work is done by a system in a thermodynamic process,its volume must increase.
In the light of the above statements,choose the correct answer from the options given below.
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 |
Heat is applied to a rigid diatomic gas at constant pressure. The ratio $\Delta Q : \Delta U : \Delta W$ is
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