Question

A solid of mass 150 g at 200°C is placed in 0.4 kg of water at 20°C till a constant temperature is attained. the S.H.C. of the solid is 0.5 Jg⁻¹ K⁻¹, find the resulting temperature of the mixture.

Answer 1

Mass of solid, m_s = 150 g

Specific heat capacity of solid, c_s = 0.5 Jg⁻¹ K⁻¹

initial temperature of solid = 200°C

Mass of water, m_w = 0.4 kg = 400 g

Specific heat capacity of water, c_w = 4.2 J g⁻¹°C⁻¹

Initial temperature of water = 20°C

Let the final temperature be T°C.

Heat lost by the solid = 150 × 0.5 × (200 − T) = (15000 − 75T) J

Heat gained by water = 400 × 4.2 × (T − 20) = (1680 T − 33600) J

Using the principle of the method of mixtures:

15000 − 75T = 1680T − 33600

1755T = 48600

T = 27.7°C

Hence, the resulting temperature of the mixture is 27.7°C.