Draw $P-V$ curves for isothermal and adiabatic processes of an ideal gas.
(N/A) The $P-V$ diagram represents a Carnot cycle,which consists of two isothermal processes and two adiabatic processes.
$1$. Isothermal expansion: The gas expands at a constant temperature.
$2$. Adiabatic expansion: The gas expands without any heat exchange with the surroundings.
$3$. Isothermal compression: The gas is compressed at a constant temperature.
$4$. Adiabatic compression: The gas is compressed without any heat exchange with the surroundings.
The adiabatic curves are steeper than the isothermal curves because the adiabatic bulk modulus is $\gamma$ times the isothermal bulk modulus,where $\gamma > 1$.
$1$. Isothermal expansion: The gas expands at a constant temperature.
$2$. Adiabatic expansion: The gas expands without any heat exchange with the surroundings.
$3$. Isothermal compression: The gas is compressed at a constant temperature.
$4$. Adiabatic compression: The gas is compressed without any heat exchange with the surroundings.
The adiabatic curves are steeper than the isothermal curves because the adiabatic bulk modulus is $\gamma$ times the isothermal bulk modulus,where $\gamma > 1$.
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Similar Questions
One mole of a monatomic ideal gas undergoes the cyclic process $J \rightarrow K \rightarrow L \rightarrow M \rightarrow J$,as shown in the $P - T$ diagram. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option. [$R$ is the gas constant]
$List-I$ $List-II$ $(P)$ Work done in the complete cyclic process $(1)$ $R T_0 - 4 R T_0 \ln 2$ $(Q)$ Change in the internal energy of the gas in the process $JK$ $(2)$ $0$ $(R)$ Heat given to the gas in the process $KL$ $(3)$ $3 R T_0$ $(S)$ Change in the internal energy of the gas in the process $MJ$ $(4)$ $-2 R T_0 \ln 2$ $(5)$ $-3 R T_0 \ln 2$
| $List-I$ | $List-II$ |
| $(P)$ Work done in the complete cyclic process | $(1)$ $R T_0 - 4 R T_0 \ln 2$ |
| $(Q)$ Change in the internal energy of the gas in the process $JK$ | $(2)$ $0$ |
| $(R)$ Heat given to the gas in the process $KL$ | $(3)$ $3 R T_0$ |
| $(S)$ Change in the internal energy of the gas in the process $MJ$ | $(4)$ $-2 R T_0 \ln 2$ |
| $(5)$ $-3 R T_0 \ln 2$ |
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 three processes in a thermodynamic cycle shown in the figure are: Process $1 \rightarrow 2$ is isothermal; Process $2 \rightarrow 3$ is isochoric (volume remains constant); Process $3 \rightarrow 1$ is adiabatic. The total work done by the ideal gas in this cycle is $10 \, J$. The internal energy decreases by $20 \, J$ in the isochoric process. The work done by the gas in the adiabatic process is $-20 \, J$. The heat added to the system in the isothermal process is .............. $J$.
MediumKVPY 2013
View SolutionWhat are the limitations of the first law of thermodynamics?
Difficult
View SolutionTwo identical vessels $A$ and $B$ contain equal amounts of an ideal monoatomic gas. The piston of $A$ is fixed,while the piston of $B$ is free to move. The same amount of heat $\Delta Q$ is absorbed by both $A$ and $B$. If the internal energy of $B$ increases by $100 \, J$,what is the change in the internal energy of $A$ (in $, J$)?
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