148106
We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?
1 $\Delta \mathrm{U}=-\mathrm{W}$ an adiabatic process
2 $\Delta \mathrm{U}=\mathrm{W}$ in an isothermal process
3 $\Delta \mathrm{U}=-\mathrm{W}$ in an isothermal process
4 $\Delta \mathrm{U}=\mathrm{W}$ in an adiabatic process
Explanation:
A From adiabatic process, $\mathrm{Q}=0$ $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dU}=\mathrm{dQ}-\mathrm{W}=0-\mathrm{W}$ $\mathrm{d} \mathrm{U}=-\mathrm{W}$ From isothermal process, $\mathrm{T}=$ constant $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{V}} \mathrm{dT}+\mathrm{W}$ $\mathrm{dQ}=0+\mathrm{W}$ $\mathrm{dQ}=\mathrm{W}$ and $\mathrm{dU}=0$
SCRA-2012
Thermodynamics
148108
If $\mathrm{R}$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to 373 $K$ when no work is done is
1 $100 \mathrm{R}$
2 $150 \mathrm{R}$
3 $300 \mathrm{R}$
4 $500 \mathrm{R}$
Explanation:
C Given, $\mathrm{n}=2$ moles, $\Delta \mathrm{T}=(373-273)=100 \mathrm{~K}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}, \gamma=1.67$ We know that, $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{dU}+0$ $\mathrm{dQ}=\mathrm{dU}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\mathrm{dQ}=2 \times \frac{3}{2} \mathrm{R} \times 100$ $\mathrm{dQ}=300 \mathrm{R}$
COMEDK 2016
Thermodynamics
148110
One mole of an ideal gas requires $207 \mathrm{~J}$ heat to raise the temperature by $10 \mathrm{~K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{~K}$, then the heat required is
1 $198.7 \mathrm{~J}$
2 $215.3 \mathrm{~J}$
3 $124 \mathrm{~J}$
4 $24 \mathrm{~J}$
Explanation:
C Given, $\mathrm{n}=1$ mole, $\mathrm{P}=$ const, $\Delta \mathrm{T}=10 \mathrm{~K}$ We know that, At constant pressure- $\mathrm{Q}_{\mathrm{P}}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}$ and at constant volume, $\mathrm{Q}_{\mathrm{V}}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\because \quad \frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}}{\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}$ $\frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{3 / 2 \mathrm{R}}{5 / 2 \mathrm{R}}$ $\mathrm{Q}_{\mathrm{V}}=\frac{3}{5} \mathrm{Q}_{\mathrm{P}}=\frac{3}{5} \times 207=124.2 \mathrm{~J}$ $\mathrm{Q}_{\mathrm{V}}=124.2 \mathrm{~J} \approx 124 \mathrm{~J}$
COMEDK-2019
Thermodynamics
148112
Assertion: Zeroth law of thermodynamics explain the concept of energy. Reason: Energy doesn't depends on temperature.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D The concept of temperature comes from the zeroth law of thermodynamic. Zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, also they are in equilibrium with each other. Energy is dependent on temperature.
AIIMS-27.05.2018(M)
Thermodynamics
148113
Assertion: The heat supplied to a system is always equal to the increase in its internal energy. Reason: When a system change from one thermal equilibrium to another, some heat is absorbed by it.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D For first law of thermodynamics, $\mathrm{dQ}=\mathrm{dU}+\mathrm{PdV}$ If heat is supplied in such a manner that volume does not change $(\mathrm{dV}=0)$ then work done (W ) Zero heat energy supplied to the system will increase internal energy only. $\mathrm{dQ}=\mathrm{PdV}$ Thermal equilibrium is no flow of heat from one portion of the system to another. Because if the temperature of the system remains constant. Hence, if both the Assertion and reason are in incorrect.
148106
We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?
1 $\Delta \mathrm{U}=-\mathrm{W}$ an adiabatic process
2 $\Delta \mathrm{U}=\mathrm{W}$ in an isothermal process
3 $\Delta \mathrm{U}=-\mathrm{W}$ in an isothermal process
4 $\Delta \mathrm{U}=\mathrm{W}$ in an adiabatic process
Explanation:
A From adiabatic process, $\mathrm{Q}=0$ $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dU}=\mathrm{dQ}-\mathrm{W}=0-\mathrm{W}$ $\mathrm{d} \mathrm{U}=-\mathrm{W}$ From isothermal process, $\mathrm{T}=$ constant $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{V}} \mathrm{dT}+\mathrm{W}$ $\mathrm{dQ}=0+\mathrm{W}$ $\mathrm{dQ}=\mathrm{W}$ and $\mathrm{dU}=0$
SCRA-2012
Thermodynamics
148108
If $\mathrm{R}$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to 373 $K$ when no work is done is
1 $100 \mathrm{R}$
2 $150 \mathrm{R}$
3 $300 \mathrm{R}$
4 $500 \mathrm{R}$
Explanation:
C Given, $\mathrm{n}=2$ moles, $\Delta \mathrm{T}=(373-273)=100 \mathrm{~K}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}, \gamma=1.67$ We know that, $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{dU}+0$ $\mathrm{dQ}=\mathrm{dU}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\mathrm{dQ}=2 \times \frac{3}{2} \mathrm{R} \times 100$ $\mathrm{dQ}=300 \mathrm{R}$
COMEDK 2016
Thermodynamics
148110
One mole of an ideal gas requires $207 \mathrm{~J}$ heat to raise the temperature by $10 \mathrm{~K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{~K}$, then the heat required is
1 $198.7 \mathrm{~J}$
2 $215.3 \mathrm{~J}$
3 $124 \mathrm{~J}$
4 $24 \mathrm{~J}$
Explanation:
C Given, $\mathrm{n}=1$ mole, $\mathrm{P}=$ const, $\Delta \mathrm{T}=10 \mathrm{~K}$ We know that, At constant pressure- $\mathrm{Q}_{\mathrm{P}}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}$ and at constant volume, $\mathrm{Q}_{\mathrm{V}}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\because \quad \frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}}{\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}$ $\frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{3 / 2 \mathrm{R}}{5 / 2 \mathrm{R}}$ $\mathrm{Q}_{\mathrm{V}}=\frac{3}{5} \mathrm{Q}_{\mathrm{P}}=\frac{3}{5} \times 207=124.2 \mathrm{~J}$ $\mathrm{Q}_{\mathrm{V}}=124.2 \mathrm{~J} \approx 124 \mathrm{~J}$
COMEDK-2019
Thermodynamics
148112
Assertion: Zeroth law of thermodynamics explain the concept of energy. Reason: Energy doesn't depends on temperature.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D The concept of temperature comes from the zeroth law of thermodynamic. Zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, also they are in equilibrium with each other. Energy is dependent on temperature.
AIIMS-27.05.2018(M)
Thermodynamics
148113
Assertion: The heat supplied to a system is always equal to the increase in its internal energy. Reason: When a system change from one thermal equilibrium to another, some heat is absorbed by it.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D For first law of thermodynamics, $\mathrm{dQ}=\mathrm{dU}+\mathrm{PdV}$ If heat is supplied in such a manner that volume does not change $(\mathrm{dV}=0)$ then work done (W ) Zero heat energy supplied to the system will increase internal energy only. $\mathrm{dQ}=\mathrm{PdV}$ Thermal equilibrium is no flow of heat from one portion of the system to another. Because if the temperature of the system remains constant. Hence, if both the Assertion and reason are in incorrect.
148106
We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?
1 $\Delta \mathrm{U}=-\mathrm{W}$ an adiabatic process
2 $\Delta \mathrm{U}=\mathrm{W}$ in an isothermal process
3 $\Delta \mathrm{U}=-\mathrm{W}$ in an isothermal process
4 $\Delta \mathrm{U}=\mathrm{W}$ in an adiabatic process
Explanation:
A From adiabatic process, $\mathrm{Q}=0$ $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dU}=\mathrm{dQ}-\mathrm{W}=0-\mathrm{W}$ $\mathrm{d} \mathrm{U}=-\mathrm{W}$ From isothermal process, $\mathrm{T}=$ constant $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{V}} \mathrm{dT}+\mathrm{W}$ $\mathrm{dQ}=0+\mathrm{W}$ $\mathrm{dQ}=\mathrm{W}$ and $\mathrm{dU}=0$
SCRA-2012
Thermodynamics
148108
If $\mathrm{R}$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to 373 $K$ when no work is done is
1 $100 \mathrm{R}$
2 $150 \mathrm{R}$
3 $300 \mathrm{R}$
4 $500 \mathrm{R}$
Explanation:
C Given, $\mathrm{n}=2$ moles, $\Delta \mathrm{T}=(373-273)=100 \mathrm{~K}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}, \gamma=1.67$ We know that, $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{dU}+0$ $\mathrm{dQ}=\mathrm{dU}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\mathrm{dQ}=2 \times \frac{3}{2} \mathrm{R} \times 100$ $\mathrm{dQ}=300 \mathrm{R}$
COMEDK 2016
Thermodynamics
148110
One mole of an ideal gas requires $207 \mathrm{~J}$ heat to raise the temperature by $10 \mathrm{~K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{~K}$, then the heat required is
1 $198.7 \mathrm{~J}$
2 $215.3 \mathrm{~J}$
3 $124 \mathrm{~J}$
4 $24 \mathrm{~J}$
Explanation:
C Given, $\mathrm{n}=1$ mole, $\mathrm{P}=$ const, $\Delta \mathrm{T}=10 \mathrm{~K}$ We know that, At constant pressure- $\mathrm{Q}_{\mathrm{P}}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}$ and at constant volume, $\mathrm{Q}_{\mathrm{V}}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\because \quad \frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}}{\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}$ $\frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{3 / 2 \mathrm{R}}{5 / 2 \mathrm{R}}$ $\mathrm{Q}_{\mathrm{V}}=\frac{3}{5} \mathrm{Q}_{\mathrm{P}}=\frac{3}{5} \times 207=124.2 \mathrm{~J}$ $\mathrm{Q}_{\mathrm{V}}=124.2 \mathrm{~J} \approx 124 \mathrm{~J}$
COMEDK-2019
Thermodynamics
148112
Assertion: Zeroth law of thermodynamics explain the concept of energy. Reason: Energy doesn't depends on temperature.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D The concept of temperature comes from the zeroth law of thermodynamic. Zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, also they are in equilibrium with each other. Energy is dependent on temperature.
AIIMS-27.05.2018(M)
Thermodynamics
148113
Assertion: The heat supplied to a system is always equal to the increase in its internal energy. Reason: When a system change from one thermal equilibrium to another, some heat is absorbed by it.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D For first law of thermodynamics, $\mathrm{dQ}=\mathrm{dU}+\mathrm{PdV}$ If heat is supplied in such a manner that volume does not change $(\mathrm{dV}=0)$ then work done (W ) Zero heat energy supplied to the system will increase internal energy only. $\mathrm{dQ}=\mathrm{PdV}$ Thermal equilibrium is no flow of heat from one portion of the system to another. Because if the temperature of the system remains constant. Hence, if both the Assertion and reason are in incorrect.
148106
We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?
1 $\Delta \mathrm{U}=-\mathrm{W}$ an adiabatic process
2 $\Delta \mathrm{U}=\mathrm{W}$ in an isothermal process
3 $\Delta \mathrm{U}=-\mathrm{W}$ in an isothermal process
4 $\Delta \mathrm{U}=\mathrm{W}$ in an adiabatic process
Explanation:
A From adiabatic process, $\mathrm{Q}=0$ $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dU}=\mathrm{dQ}-\mathrm{W}=0-\mathrm{W}$ $\mathrm{d} \mathrm{U}=-\mathrm{W}$ From isothermal process, $\mathrm{T}=$ constant $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{V}} \mathrm{dT}+\mathrm{W}$ $\mathrm{dQ}=0+\mathrm{W}$ $\mathrm{dQ}=\mathrm{W}$ and $\mathrm{dU}=0$
SCRA-2012
Thermodynamics
148108
If $\mathrm{R}$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to 373 $K$ when no work is done is
1 $100 \mathrm{R}$
2 $150 \mathrm{R}$
3 $300 \mathrm{R}$
4 $500 \mathrm{R}$
Explanation:
C Given, $\mathrm{n}=2$ moles, $\Delta \mathrm{T}=(373-273)=100 \mathrm{~K}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}, \gamma=1.67$ We know that, $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{dU}+0$ $\mathrm{dQ}=\mathrm{dU}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\mathrm{dQ}=2 \times \frac{3}{2} \mathrm{R} \times 100$ $\mathrm{dQ}=300 \mathrm{R}$
COMEDK 2016
Thermodynamics
148110
One mole of an ideal gas requires $207 \mathrm{~J}$ heat to raise the temperature by $10 \mathrm{~K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{~K}$, then the heat required is
1 $198.7 \mathrm{~J}$
2 $215.3 \mathrm{~J}$
3 $124 \mathrm{~J}$
4 $24 \mathrm{~J}$
Explanation:
C Given, $\mathrm{n}=1$ mole, $\mathrm{P}=$ const, $\Delta \mathrm{T}=10 \mathrm{~K}$ We know that, At constant pressure- $\mathrm{Q}_{\mathrm{P}}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}$ and at constant volume, $\mathrm{Q}_{\mathrm{V}}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\because \quad \frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}}{\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}$ $\frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{3 / 2 \mathrm{R}}{5 / 2 \mathrm{R}}$ $\mathrm{Q}_{\mathrm{V}}=\frac{3}{5} \mathrm{Q}_{\mathrm{P}}=\frac{3}{5} \times 207=124.2 \mathrm{~J}$ $\mathrm{Q}_{\mathrm{V}}=124.2 \mathrm{~J} \approx 124 \mathrm{~J}$
COMEDK-2019
Thermodynamics
148112
Assertion: Zeroth law of thermodynamics explain the concept of energy. Reason: Energy doesn't depends on temperature.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D The concept of temperature comes from the zeroth law of thermodynamic. Zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, also they are in equilibrium with each other. Energy is dependent on temperature.
AIIMS-27.05.2018(M)
Thermodynamics
148113
Assertion: The heat supplied to a system is always equal to the increase in its internal energy. Reason: When a system change from one thermal equilibrium to another, some heat is absorbed by it.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D For first law of thermodynamics, $\mathrm{dQ}=\mathrm{dU}+\mathrm{PdV}$ If heat is supplied in such a manner that volume does not change $(\mathrm{dV}=0)$ then work done (W ) Zero heat energy supplied to the system will increase internal energy only. $\mathrm{dQ}=\mathrm{PdV}$ Thermal equilibrium is no flow of heat from one portion of the system to another. Because if the temperature of the system remains constant. Hence, if both the Assertion and reason are in incorrect.
148106
We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?
1 $\Delta \mathrm{U}=-\mathrm{W}$ an adiabatic process
2 $\Delta \mathrm{U}=\mathrm{W}$ in an isothermal process
3 $\Delta \mathrm{U}=-\mathrm{W}$ in an isothermal process
4 $\Delta \mathrm{U}=\mathrm{W}$ in an adiabatic process
Explanation:
A From adiabatic process, $\mathrm{Q}=0$ $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dU}=\mathrm{dQ}-\mathrm{W}=0-\mathrm{W}$ $\mathrm{d} \mathrm{U}=-\mathrm{W}$ From isothermal process, $\mathrm{T}=$ constant $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{V}} \mathrm{dT}+\mathrm{W}$ $\mathrm{dQ}=0+\mathrm{W}$ $\mathrm{dQ}=\mathrm{W}$ and $\mathrm{dU}=0$
SCRA-2012
Thermodynamics
148108
If $\mathrm{R}$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to 373 $K$ when no work is done is
1 $100 \mathrm{R}$
2 $150 \mathrm{R}$
3 $300 \mathrm{R}$
4 $500 \mathrm{R}$
Explanation:
C Given, $\mathrm{n}=2$ moles, $\Delta \mathrm{T}=(373-273)=100 \mathrm{~K}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}, \gamma=1.67$ We know that, $\mathrm{dQ}=\mathrm{dU}+\mathrm{W}$ $\mathrm{dQ}=\mathrm{dU}+0$ $\mathrm{dQ}=\mathrm{dU}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\mathrm{dQ}=2 \times \frac{3}{2} \mathrm{R} \times 100$ $\mathrm{dQ}=300 \mathrm{R}$
COMEDK 2016
Thermodynamics
148110
One mole of an ideal gas requires $207 \mathrm{~J}$ heat to raise the temperature by $10 \mathrm{~K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{~K}$, then the heat required is
1 $198.7 \mathrm{~J}$
2 $215.3 \mathrm{~J}$
3 $124 \mathrm{~J}$
4 $24 \mathrm{~J}$
Explanation:
C Given, $\mathrm{n}=1$ mole, $\mathrm{P}=$ const, $\Delta \mathrm{T}=10 \mathrm{~K}$ We know that, At constant pressure- $\mathrm{Q}_{\mathrm{P}}=\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}$ and at constant volume, $\mathrm{Q}_{\mathrm{V}}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\because \quad \frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}}{\mathrm{nC}_{\mathrm{P}} \Delta \mathrm{T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}$ For monatomic gas, $\mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R}$ and $\mathrm{C}_{\mathrm{P}}=\frac{5}{2} \mathrm{R}$ $\frac{\mathrm{Q}_{\mathrm{V}}}{\mathrm{Q}_{\mathrm{P}}}=\frac{3 / 2 \mathrm{R}}{5 / 2 \mathrm{R}}$ $\mathrm{Q}_{\mathrm{V}}=\frac{3}{5} \mathrm{Q}_{\mathrm{P}}=\frac{3}{5} \times 207=124.2 \mathrm{~J}$ $\mathrm{Q}_{\mathrm{V}}=124.2 \mathrm{~J} \approx 124 \mathrm{~J}$
COMEDK-2019
Thermodynamics
148112
Assertion: Zeroth law of thermodynamics explain the concept of energy. Reason: Energy doesn't depends on temperature.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D The concept of temperature comes from the zeroth law of thermodynamic. Zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, also they are in equilibrium with each other. Energy is dependent on temperature.
AIIMS-27.05.2018(M)
Thermodynamics
148113
Assertion: The heat supplied to a system is always equal to the increase in its internal energy. Reason: When a system change from one thermal equilibrium to another, some heat is absorbed by it.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
D For first law of thermodynamics, $\mathrm{dQ}=\mathrm{dU}+\mathrm{PdV}$ If heat is supplied in such a manner that volume does not change $(\mathrm{dV}=0)$ then work done (W ) Zero heat energy supplied to the system will increase internal energy only. $\mathrm{dQ}=\mathrm{PdV}$ Thermal equilibrium is no flow of heat from one portion of the system to another. Because if the temperature of the system remains constant. Hence, if both the Assertion and reason are in incorrect.
