$A$ reversible cyclic process for an ideal gas is shown below. Here,$P, V$,and $T$ are pressure,volume,and temperature,respectively. The thermodynamic parameters $q, w, H$,and $U$ are heat,work,enthalpy,and internal energy,respectively.
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{AC}$ and $W_{AB} = 0$
$(B)$ $W_{BC} = P_2(V_1 - V_2)$ and $q_{BC} = \Delta H_{BC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{AC}$
$(D)$ $q_{BC} = \Delta H_{BC}$ and $\Delta H_{CA} > \Delta U_{CA}$
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{AC}$ and $W_{AB} = 0$
$(B)$ $W_{BC} = P_2(V_1 - V_2)$ and $q_{BC} = \Delta H_{BC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{AC}$
$(D)$ $q_{BC} = \Delta H_{BC}$ and $\Delta H_{CA} > \Delta U_{CA}$
- A$(A), (B)$
- B$(A), (C)$
- C$(B), (C)$
- D$(B), (D)$
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Consider an engine that absorbs $130 \text{ cal}$ of heat from a hot reservoir and delivers $30 \text{ cal}$ of heat to a cold reservoir in each cycle. The engine also consumes $2 \text{ J}$ of energy in each cycle to overcome friction. If the engine works at $90 \text{ cycles per minute}$, what will be the maximum power delivered to the load (in $\text{ W}$)? [Assume the thermal equivalent of heat is $4.2 \text{ J/cal}$]
MediumWBJEE 2020
View Solution$List-I$ 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?
Match the "Technology" given in List-$1$ with the "Principle of Physics" given in List-$2$.
$A$. Steam engine $I$. Magnetic confinement of plasma $B$. Electron microscope $II$. Laws of thermodynamics $C$. Non-reflecting coatings $III$. Wave nature of electrons $D$. Tokamak $IV$. Interference of light
| $A$. Steam engine | $I$. Magnetic confinement of plasma |
| $B$. Electron microscope | $II$. Laws of thermodynamics |
| $C$. Non-reflecting coatings | $III$. Wave nature of electrons |
| $D$. Tokamak | $IV$. Interference of light |
An ideal gas at pressure $P$ and volume $V$ is expanded to volume $2V$. Column $I$ represents the thermodynamic processes used during expansion. Column $II$ represents the work done during these processes in random order:
Column $I$ Column $II$ $(p)$ isobaric $(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$ $(q)$ isothermal $(y)$ $PV$ $(r)$ adiabatic $(z)$ $PV \ln 2$
The correct matching of column $I$ and column $II$ is given by:
| Column $I$ | Column $II$ |
| $(p)$ isobaric | $(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$ |
| $(q)$ isothermal | $(y)$ $PV$ |
| $(r)$ adiabatic | $(z)$ $PV \ln 2$ |
The correct matching of column $I$ and column $II$ is given by:
Difficult
View Solution$A$ given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be $0.75$ of its initial pressure. The ratio of the specific heats of the gas is approximately:
DifficultTS EAMCET 2006
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