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(B) The molar heat capacity $C$ is defined by the relation $dQ = \mu C dT$,where $\mu$ is the number of moles and $dT$ is the change in temperature.Th

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$3\,R$

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(B) The molar heat capacity $C$ is defined by the relation $dQ = \mu C dT$,where $\mu$ is the number of moles and $dT$ is the change in temperature.The internal energy change for an ideal gas is given by $dU = \mu C_v dT$.Given the process equation: $dQ = 2dU$.Substituting the expressions for $dQ$ and $dU$:$\mu C dT = 2(\mu C_v dT)$Dividing both sides by $\mu dT$:$C = 2C_v$For a monoatomic gas,the molar heat capacity at constant volume is $C_v = \frac{3}{2}R$.Therefore,$C = 2 	imes (\frac{3}{2}R) = 3R$.The molar heat capacity for the process is $3R$.

List-$I$	List-$II$
$(A)$ Isothermal	$(I)$ $\Delta W = 0$
$(B)$ Adiabatic	$(II)$ $\Delta Q = 0$
$(C)$ Isobaric	$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric	$(IV)$ $\Delta U = 0$

An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

Similar Questions

Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(A)$ Isothermal $(I)$ $\Delta W = 0$
$(B)$ Adiabatic $(II)$ $\Delta Q = 0$
$(C)$ Isobaric $(III)$ $\Delta U \neq 0$
$(D)$ Isochoric $(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

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One mole of an ideal monoatomic gas is heated at a constant pressure of one atmosphere from $0^{\circ}C$ to $100^{\circ}C$. Then the change in the internal energy is

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$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

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