One mole of diatomic gas having rotational mo | vedclass

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

Question

(B) For a diatomic gas with rotational modes only, the degrees of freedom $f = 5$ ($3$ translational + $2$ rotational). Thus, $C_v = \frac{f}{2}R = \f

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(B) For a diatomic gas with rotational modes only, the degrees of freedom $f = 5$ ($3$ translational + $2$ rotational). Thus, $C_v = \frac{f}{2}R = \frac{5}{2}R$.Change in internal energy $\Delta U = nC_v \Delta T = 1 	imes \frac{5}{2} 	imes 8.3 	imes 1.2 = 24.9 	ext{ J}$.Work done by the gas $W = P \Delta V = P(A \Delta x)$.Given $P = 10^5 	ext{ Pa}$, $A = 4 	imes 10^{-4} 	ext{ m}^2$, and $\Delta x = 25 	imes 10^{-3} 	ext{ m}$.$W = 10^5 	imes 4 	imes 10^{-4} 	imes 25 	imes 10^{-3} = 1 	ext{ J}$.Total heat supplied $Q = \Delta U + W = 24.9 + 1 = 25.9 	ext{ J}$.Comparing with the given options, $25 	ext{ J}$ is the closest value.

Similar Questions

$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is $\left(\gamma = \frac{5}{3}\right)$.

$A$ bubble containing $8$ moles of Helium is submerged at a certain depth in water. When the temperature of the water increases by $30 \ ^\circ C$,how much heat in $J$ is added during the expansion of the Helium bubble?

Which of the following statement$(s)$ is/are true? "Internal energy of an ideal gas ..........."

$A$ monoatomic gas at pressure $P$,having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (Take $\gamma = 5/3$)

In a certain thermodynamical process,the pressure of a gas depends on its volume as $P = kV^{3}$. The work done when the temperature changes from $100^{\circ}C$ to $300^{\circ}C$ will be .......... $nR$,where $n$ denotes the number of moles of a gas.

Vedclass Test Series

Exam Paper Generator

Online Exam Module