A 200 g sample of water with a temperature of 32◦C is added to 50 g water at 55◦C in an insulated container. What is the final temperature after thermal equilibrium is reached? The specific heat of water in the liquid state is 4.18 J/g◦C, in the solid state is 2.09 J/g◦C, and in the gaseous state is 2.03 J/g◦C. The heat of fusion is 334 J/g and the heat of vaporization is 2260 J/g. 1. 49.2◦C 2. 36.6◦C 3. 52.6◦C 4. 38.4◦C 5. 50.4◦C 6. 43.5◦C 7. 34.1◦C

2. 36.6°C.

Explanation:

∵ The amount of heat released by hot water = amount of heat absorbed by cold water.

• The amount of heat released by hot water = Q hot water = - m. c.ΔT.

where, m is the mass of hot water = 50 g.

c is the specific heat capacity of liquid water = 4.18 J/g°C.

ΔT is the temperature difference = (final T - initial T = final T - 55°C).

• The amount of heat absorbed by cold water = Q cold water = m. c.ΔT.

where, m is the mass of cold water = 200 g.

c is the specific heat capacity of liquid water = 4.18 J/g°C.

ΔT is the temperature difference = (final T - initial T = final T - 32°C).

∵ Q hot water = Q cold water

∴ ( - m. c.ΔT) hot water = (m. c.ΔT) cold water

∴ ( - m.ΔT) hot water = (m.ΔT) cold water

- (50 g) (final T - 55°C) = (200 g) (final T - 32°C)

-50 final T + 2750 = 200 final T - 6400

250 final T = 2750 + 6400 = 9150

∴ final T = 9150/250 = 36.6°C.