An ideal gas undergoes isothermal compression | vedclass

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Question

(C) The work done on the gas during compression is $W = -P_{ext} \Delta V$.Since the process is isothermal,the heat released by the gas is equal to th

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$\frac{2}{3}\, K$

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(C) The work done on the gas during compression is $W = -P_{ext} \Delta V$.Since the process is isothermal,the heat released by the gas is equal to the magnitude of work done on the surroundings,$q = P_{ext} \Delta V$.Given $P_{ext} = 4\, Nm^{-2}$,$V_1 = 5\, m^3$,and $V_2 = 1\, m^3$,the change in volume is $\Delta V = V_1 - V_2 = 5 - 1 = 4\, m^3$.Thus,$q = 4\, Nm^{-2} 	imes 4\, m^3 = 16\, J$.This heat is used to heat $1\, mole$ of $Al$ with molar heat capacity $C = 24\, J\, mol^{-1}\, K^{-1}$.Using the formula $q = n C \Delta T$,we have $\Delta T = \frac{q}{n C}$.$\Delta T = \frac{16}{1 	imes 24} = \frac{2}{3}\, K$.

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