# A metal ball of mass 0.1 kg is heated upto 500°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 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg−1K−1 and  400 Jkg−1K−1] a. 30% b. 20% c. 25% d. 15%

## Question ID - 50600 | SaraNextGen Top Answer A metal ball of mass 0.1 kg is heated upto 500°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 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg−1K−1 and  400 Jkg−1K−1] a. 30% b. 20% c. 25% d. 15%

Answer Key / Explanation : (b) -

0.1 × 400 × (500 − T) = 0.5 × 4200 × (T − 30) + 800 (T − 30)

⇒ 40(500 − T) = (T − 30) (2100 + 800)

⇒20000 − 40T = 2900 T − 30 × 2900

⇒20000 + 30 × 2900 = T(2940)

T = 30.4°C

× 100 =  × 100

= 20%