Given below are two statements: one is labell | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Statement $I$ is correct. The change in internal energy for an ideal gas is given by $\Delta U = nC_v \Delta T$. Since $C_v = \frac{R}{\gamma - 1}

Vedclass · Accepted Answer

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Vedclass · Answer

(A) Statement $I$ is correct. The change in internal energy for an ideal gas is given by $\Delta U = nC_v \Delta T$. Since $C_v = \frac{R}{\gamma - 1}$, substituting this gives $\Delta U = \frac{nR}{\gamma - 1}(T_f - T_i)$.Statement $II$ is also correct. The molar heat capacity at constant volume is $C_v = \frac{fR}{2}$ and at constant pressure is $C_p = C_v + R = (\frac{f}{2} + 1)R$. Therefore, $\gamma = \frac{C_p}{C_v} = \frac{(\frac{f}{2} + 1)R}{\frac{fR}{2}} = \frac{f+2}{f} = 1 + \frac{2}{f}$.Since both statements are true and the definition of $\gamma$ in terms of $f$ is a fundamental property used to derive the expression in Statement $I$, $R$ is the correct explanation of $A$.

Similar Questions

An insulated box containing a diatomic gas of molar mass $M$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

Two vessels of the same volume contain the same gas at the same temperature. If the pressure in the vessels is in the ratio of $1 : 2$,then

$A$ cylinder of fixed capacity $44.8 \, L$ contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $15.0 \, ^{\circ}C$? $(R = 8.31 \, J \, mol^{-1} K^{-1})$

Two thermally insulated vessels $1$ and $2$ contain air at temperatures $(T_1, T_2)$,volumes $(V_1, V_2)$,and pressures $(P_1, P_2)$. If the valve connecting them is opened,what will be the equilibrium temperature of the system?

From a certain apparatus,the diffusion rate of hydrogen has an average value of $28.7 \; cm^3 s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of $7.2 \; cm^3 s^{-1}$. Identify the gas.

Vedclass Test Series

Exam Paper Generator

Online Exam Module