(B) Heat added at constant volume is equal to the change in internal energy of the system. The change in internal energy is given by $\Delta U = n C_{

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(B) Heat added at constant volume is equal to the change in internal energy of the system. The change in internal energy is given by $\Delta U = n C_{v} \Delta T$.For $\Delta T = 150 \ K$,the change in internal energy is $\Delta U = Q_{v} = 6300 \ J$.Therefore,$6300 = n C_{v} (150) \quad \dots(1)$.We need to find the change in internal energy $\Delta U'$ for $\Delta T' = 300 \ K$.Thus,$\Delta U' = n C_{v} (300) \quad \dots(2)$.Dividing equation $(2)$ by equation $(1)$,we get $\frac{\Delta U'}{6300} = \frac{300}{150} = 2$.Therefore,$\Delta U' = 6300 \times 2 = 12600 \ J$.

Class 11 Physics Thermodynamics First Law of Thermodynamics

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If heat is added at constant volume,$6300 \ J$ of heat are required to raise the temperature of an ideal gas by $150 \ K$. If instead,heat is added at constant pressure,$8800 \ J$ are required for the same temperature change. When the temperature of the gas changes by $300 \ K$,the internal energy of the gas changes by ..... $J$.

A
$5000$
B
$12600$
C
$17600$
D
$22600$

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Class 11

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Thermodynamics

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First Law of Thermodynamics

$A$ resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. $A$ current $i$ flows through the coil which has a resistance $R$. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.

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$A$ system performs work $\Delta W$ when an amount of heat $\Delta Q$ is added to the system. The corresponding change in the internal energy is $\Delta U$. Which of the following is a unique function of the initial and final states (irrespective of the mode of change)?

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$A$ diatomic gas has an initial internal energy of $80 cal$. $A$ work of $18 cal$ is done on the gas and the gas releases heat energy of $42 J$. The final internal energy of the gas is

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State the first law of thermodynamics and write its limitations.

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In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20 \, J$ of heat when $8 \, J$ of work is done on the gas. If the initial internal energy of the gas was $30 \, J$,then the final internal energy will be .... $J$.

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$A$ system performs work $\Delta W$ when an amount of heat $\Delta Q$ is added to the system. The corresponding change in the internal energy is $\Delta U$. Which of the following is a unique function of the initial and final states (irrespective of the mode of change)?

$A$ diatomic gas has an initial internal energy of $80 cal$. $A$ work of $18 cal$ is done on the gas and the gas releases heat energy of $42 J$. The final internal energy of the gas is

State the first law of thermodynamics and write its limitations.

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20 \, J$ of heat when $8 \, J$ of work is done on the gas. If the initial internal energy of the gas was $30 \, J$,then the final internal energy will be .... $J$.

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