Question

A metallic ball of mass 200 g and at 200°C is placed over a block of ice, when 100 g of ice melts. If the specific latent heat of fusion of ice is 336 J g⁻¹, find the specific heat capacity of the metallic ball.

Answer 1

Given: Mass of the metallic ball, m = 200 g

Initial temperature of the ball, θ₁ = 200°C

Mass of ice melted, M =  100 g

Specific latent heat of fusion of ice, L = 336 J g⁻¹

The ball cools to 0°C so final temperature θ₂ = 0°C

Heat lost by the ball:

Q_lost = mc(θ₁ − θ₂)

= 200 × c × (200 − 0)

= 40000c J

Heat gained by melting ice:

$$Q_{\text{gained}} = M L$$

= 100 × 336

= 33600 J

By the principle of calorimetry,

Heat lost = Heat gained

40000c = 33600

$$c = \frac{33600}{40000}$$

c = 0.84 J g⁻¹°C⁻¹

Therefore, the specific heat capacity of the metallic ball is 0.84 J g⁻¹°C⁻¹.