A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a… | JEE Main 2019 (11 Jan, Shift 2)

Q40JEE Main 2019 · 11 JAN · SHIFT 2Medium

Calorimetry, Latent Heat & Mechanical Equivalent of Heat

A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg–1 K–1 and 400 Jkg–1 K–1]

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Answer: (a)

Ball: $mc = 0.1 \times 400 = 40\text{ J/K}$ ; water + vessel: $0.5 \times 4200 + 800 = 2900\text{ J/K}$ .
$40(500 - T) = 2900(T - 30) \Rightarrow T \approx 36.4^{\circ}\text{C}$
Percentage rise $= \dfrac{6.4}{30} \times 100 \approx 21\%$
So the answer is (a) $20\%$ .

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