Which of the following set of properties is correct when one mole of a gas is heated keeping volume constant…

Which of the following set of properties is correct when one mole of a gas is heated keeping volume constant by increasing temperature and supplying 500 J of heat?
  1. $\mathrm{q}=\mathrm{w}=500 \mathrm{~J}, \Delta \mathrm{U}=0$
  2. $\mathrm{q}=\Delta \mathrm{U}=500 \mathrm{~J}, \mathrm{w}=0$
  3. $\mathrm{q}=\Delta \mathrm{U}=-500 \mathrm{~J}, \mathrm{w}=0$
  4. $\mathrm{q}=500 \mathrm{~J}, \Delta \mathrm{U}=\mathrm{w}=0$

Solution

Heat is supplied to the system. $\therefore \quad q=500 \mathrm{~J}$
At constant volume, $\Delta \mathrm{V}=0$ $\therefore \quad \mathrm{w}=-\mathrm{P}_{\mathrm{ext}} \Delta \mathrm{~V}=0$
According to the first law of thermodynamics, $\begin{aligned} & \Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \\ & \therefore \quad \Delta U=500+0=500 \mathrm{~J} \end{aligned}$

Asked in: MHT CET 2024 (04 May Shift 1)

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