MHT CET · Chemistry · Thermodynamics (C)
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?
- A \(\mathrm{q}=\mathrm{w}=500 \mathrm{~J}, \Delta \mathrm{U}=0\)
- B \(\mathrm{q}=\Delta \mathrm{U}=500 \mathrm{~J}, \mathrm{w}=0\)
- C \(\mathrm{q}=\Delta \mathrm{U}=-500 \mathrm{~J}, \mathrm{w}=0\)
- D \(\mathrm{q}=500 \mathrm{~J}, \Delta \mathrm{U}=\mathrm{w}=0\)
Answer & Solution
Correct Answer
(B) \(\mathrm{q}=\Delta \mathrm{U}=500 \mathrm{~J}, \mathrm{w}=0\)
Step-by-step Solution
Detailed explanation
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,
\(\begin{aligned}
& \Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \\
& \therefore \quad \Delta U=500+0=500 \mathrm{~J}
\end{aligned}\)
\(\therefore \quad q=500 \mathrm{~J}\)
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,
\(\begin{aligned}
& \Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \\
& \therefore \quad \Delta U=500+0=500 \mathrm{~J}
\end{aligned}\)
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