If one mole of an ideal gas at $(P_{1}, V_{1})$ is allowed to expand reversibly and isothermally ($A$ to $B$),its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $(B \rightarrow C)$. Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net work done by the gas is equal to ...... .
- A$RT \left(\ln 2 - \frac{1}{2(\gamma-1)}\right)$
- B$-\frac{RT}{2(\gamma-1)}$
- C$0$
- D$RT \ln 2$
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Similar Questions
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.
Fill in the blanks:
$1.$ The heat required to raise the temperature of a body by $1\,K$ is called ...... .
$2.$ $A$ temperature difference of $10\,^{\circ}C$ is equivalent to a temperature difference of ...... on the Fahrenheit temperature scale.
$3.$ For an isothermal process of an ideal gas,$\frac{dP}{P} = .........$
$1.$ The heat required to raise the temperature of a body by $1\,K$ is called ...... .
$2.$ $A$ temperature difference of $10\,^{\circ}C$ is equivalent to a temperature difference of ...... on the Fahrenheit temperature scale.
$3.$ For an isothermal process of an ideal gas,$\frac{dP}{P} = .........$
Medium
View Solution$A$ gas may expand either adiabatically or isothermally. $A$ number of $P-V$ curves are drawn for the two processes over different ranges of pressure and volume. It will be found that:
Easy
View SolutionOne mole of a gas expands obeying the relation as shown in the $P-V$ diagram. The maximum temperature in this process is equal to
$List-I$ describes thermodynamic processes in four different systems. $List-II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.
$List-I$ $List-II$ $(I)$ $10^{-3} \, kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 \, Pa$. The volume of the system changes from $10^{-6} \, m^3$ to $10^{-3} \, m^3$. Latent heat of water $= 2250 \, kJ/kg$. $(P)$ $2 \, kJ$ $(II)$ $0.2 \, moles$ of a rigid diatomic ideal gas with volume $V$ at temperature $500 \, K$ undergoes an isobaric expansion to volume $3V$. Assume $R = 8.0 \, J \, mol^{-1} \, K^{-1}$. $(Q)$ $7 \, kJ$ $(III)$ One mole of a monatomic ideal gas is compressed adiabatically from volume $V = 1/3 \, m^3$ and pressure $2 \, kPa$ to volume $V/8$. $(R)$ $4 \, kJ$ $(IV)$ Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \, kJ$ of heat and undergoes isobaric expansion. $(S)$ $5 \, kJ$ $(T)$ $3 \, kJ$
Which one of the following options is correct?
| $List-I$ | $List-II$ |
| $(I)$ $10^{-3} \, kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 \, Pa$. The volume of the system changes from $10^{-6} \, m^3$ to $10^{-3} \, m^3$. Latent heat of water $= 2250 \, kJ/kg$. | $(P)$ $2 \, kJ$ |
| $(II)$ $0.2 \, moles$ of a rigid diatomic ideal gas with volume $V$ at temperature $500 \, K$ undergoes an isobaric expansion to volume $3V$. Assume $R = 8.0 \, J \, mol^{-1} \, K^{-1}$. | $(Q)$ $7 \, kJ$ |
| $(III)$ One mole of a monatomic ideal gas is compressed adiabatically from volume $V = 1/3 \, m^3$ and pressure $2 \, kPa$ to volume $V/8$. | $(R)$ $4 \, kJ$ |
| $(IV)$ Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \, kJ$ of heat and undergoes isobaric expansion. | $(S)$ $5 \, kJ$ |
| $(T)$ $3 \, kJ$ |
Which one of the following options is correct?
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