Question

A copper ball of specific heat capacity 0.9 Jg⁻¹°C⁻¹ and mass 500 g is placed on a block of ice, when 800 g of ice just melts. Find the temperature of the copper ball. [Assume specific latent heat of fusion of ice = 340 Jg⁻¹]

Answer 1

Assuming no heat loss to the surroundings and a final temperature of 0°C:

Heat lost by the copper ball = heat gained by the ice to melt.

m_ice = 800 g, L = 340 Jg⁻¹

Heat gained by ice = mL

= 800 × 340

= 272000 J

Let the initial temperature of the copper ball be T.

Heat lost by the ball = mcΔT

= 500 × 0.9 × (T − 0)

= 450 T

Heat lost = Heat gained

450 T = 272000

$$T = \frac{272000}{450}$$

T = 604.4°C

Therefore, the copper ball's temperature is about 604.4°C.