1 g of a liquid is converted to vapour at $3 \times 10^{5} \mathrm{~Pa}$ pressure. If $10\%$ of the heat supplied is used for increasing the volume by $1600 \mathrm{~cm}^{3}$ during this phase change, then the increase in internal energy in the process will be :

(D) $4.32 \times 10^{8} \mathrm{~J}$

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Heat & Thermodynamics

1 g of a liquid is converted to vapour at

3 \times 1 0^{5} Pa

pressure. If

10%

of the heat supplied is used for increasing the volume by

1600 cm^{3}

during this phase change, then the increase in internal energy in the process will be :

(A)4320 J✓ Correct
(B)432000 J
(C)4800 J
(D) $4.32 \times 1 0^{8} J$

Answer: (A)

Solution

The expansion does work

W = P Δ V = 3 \times 1 0^{5} \times 1600 \times 1 0^{- 6} = 480 J

. Since this work is only ten percent of the heat supplied, the heat delivered is

\frac{480}{0.1} = 4800 J

. The first law of thermodynamics then gives the rise in internal energy as

Δ U = Q - W = 4800 - 480 = 4320 J

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option

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