An ideal gas undergoes isothermal compression from 5 \(\mathrm{m^3}\) to 1 \(\mathrm{m^3}\) against a constant external pressure of 4 \(\mathrm{N\,m^{-2}}\). Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 \(\mathrm{J\,mol^{-1}\,K^{-1}}\), the temperature of Al increases by :
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- \(\frac{2}{3}\,\mathrm{K}\)
- \(\frac{3}{2}\,\mathrm{K}\)
- 1 K
- 2 K
The Correct Option is A
Solution and Explanation
Isothermal, ideal gas: \(\Delta U = 0\), so \(q = -w = -16\ \mathrm{J}\). The gas releases 16 J.
This heat raises the temperature of 1 mol Al: \(q = nC\Delta T\), so \(\Delta T = \frac{16}{1 \times 24} = \frac{2}{3}\ \mathrm{K}\).
Answer: (1) \(\frac{2}{3}\,\mathrm{K}\)
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