Thermodynamics

JEE Main level, single correct, medium

76 of 190

Question 76 of 190

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from T1\mathrm{T}_1 to T2\mathrm{T}_2 is proportional to (T2−T1)\left(\mathrm{T}_2-\mathrm{T}_1\right)
Choose the correct answer from the options given below :

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Answer: (C) (B), (E) only

Q=ΔU+W=0⇒−ΔU=WWD=−nCvΔT⇒∣WD∣=nCvΔT∝T2−T1\begin{aligned} & \mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}=0 \Rightarrow-\Delta \mathrm{U}=\mathrm{W} \\ & \mathrm{WD}=-\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T} \Rightarrow|\mathrm{WD}|=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T} \propto \mathrm{T}_2-\mathrm{T}_1\end{aligned}
∴B&E\therefore \mathrm{B} \& \mathrm{E} [Only possibility]

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