3 moles of an ideal monoatomic gas performs a | vedclass

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

Question

(B) For an ideal gas, the equation of state is $pV = \mu RT$, which implies $p = (\frac{\mu R}{V})T$. In a $p-T$ diagram, lines passing through the or

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) For an ideal gas, the equation of state is $pV = \mu RT$, which implies $p = (\frac{\mu R}{V})T$. In a $p-T$ diagram, lines passing through the origin represent isochoric processes (constant volume) because $p \propto T$ implies $V = 	ext{constant}$. Processes $AB$ and $CD$ are straight lines passing through the origin, so they are isochoric processes. Work done in an isochoric process is zero. Thus, $W_{AB} = 0$ and $W_{CD} = 0$. Processes $BC$ and $DA$ are isobaric processes (constant pressure). Work done in an isobaric process is $W = p\Delta V = \mu R \Delta T$. For process $BC$ (at pressure $p_2$): $W_{BC} = \mu R(T_C - T_B) = 3 	imes R 	imes (2400 - 800) = 3R 	imes 1600 = 4800R$. For process $DA$ (at pressure $p_1$): $W_{DA} = \mu R(T_A - T_D) = 3 	imes R 	imes (400 - 1200) = 3R 	imes (-800) = -2400R$. The total work done in the cycle is $W = W_{AB} + W_{BC} + W_{CD} + W_{DA} = 0 + 4800R + 0 - 2400R = 2400R$. Substituting $R = 8.314 \, J/mol \cdot K$: $W = 2400 	imes 8.314 = 19953.6 \, J \approx 20 \, kJ$.

$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

Similar Questions

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The process on the $P-V$ diagram is:

An ideal gas is heated at constant pressure. If $Q$ is the amount of heat absorbed,then the ratio of the work done to the heat absorbed for increasing the internal energy is:

$A$ monatomic gas of volume $V$ and pressure $P$ expands isothermally to a volume $27 V$ and then is compressed adiabatically to a volume $V$. The final pressure of the gas is: (in $P$)

An ideal gas is subjected to a cyclic process $A B C D$ as depicted in the $p-V$ diagram given below. Which of the following curves represents the equivalent cyclic process?

Vedclass Test Series

Exam Paper Generator

Online Exam Module