A steam engine intakes 50 g of steam at $100^{\circ}\mathrm{C}$ per minute and cools it down to $20^{\circ}\mathrm{C}$. If latent heat of vaporization of steam is $540 \mathrm{~cal~g}^{-1}$, then the heat rejected by the steam engine per minute is ______ $\times 10^3 \mathrm{~cal}$.

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Heat & Thermodynamics

A steam engine intakes 50 g of steam at

10 0^{\circ} C

per minute and cools it down to

2 0^{\circ} C

. If latent heat of vaporization of steam is

540 cal g^{- 1}

, then the heat rejected by the steam engine per minute is ______

\times 1 0^{3} cal

Answer: 31

Solution

The heat rejected consists of two parts:

Heat released during condensation: $Q_{1} = m L = 50 \times 540 = 27000$ cal
Heat released during cooling from $10 0^{\circ} C$ to $2 0^{\circ} C$ : $Q_{2} = m c Δ T = 50 \times 1 \times (100 - 20) = 4000$ cal

Total heat rejected:

Q = Q_{1} + Q_{2} = 27000 + 4000 = 31000

cal

= 31 \times 1 0^{3}

cal

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Integer answer

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