A metal bal of mass 0.1 kg is heated upto $500^{\circ} \mathrm{C}$ and dropped into a vessel of heat capacity $800 \mathrm{JK}^{-1}$ and containing 0.5 kg water. The initial temperature of water and vessel is $30^{0} \mathrm{C}$. What is the approximate percentage increment in the temperature of the water? [Specific heat Capacities of water and metal are, respectively $4200 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ and $400 \mathrm{jkg}^{-1} \mathrm{~K}^{-1}$ ]

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Heat & Thermodynamics

A metal bal of mass 0.1 kg is heated upto

50 0^{\circ} C

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

3 0^{0} C

. 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}

]

Answer: (D)

Heat released by the cooling metal ball is taken up by the water and the vessel. With final temperature

T

0.1 \times 400 \times (500 - T) = 0.5 \times 4200 \times (T - 30) + 800 (T - 30)

. The left side is

40 (500 - T)

and the right is

2900 (T - 30)

, so

20000 - 40 T = 2900 T - 87000

, giving

2940 T = 107000

and

T \approx 36. 4^{\circ}

C. The water's rise is

36.4 - 30 = 6. 4^{\circ}

C, which as a fraction of its initial

3 0^{\circ}

C is

\frac{6.4}{30} \times 100 \approx 20%

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option