50 ml of milk at 5°C is added to 200 ml of hot chocolate at 95°C. What do you think the approximate new temperature is?

Answer;

76.3°C

Explanation;

Considering the fact that;

Specific heat capacity of the hot chocolate = 3.751 kJ/kg C°

Specific heat capacity of milk is 3.93 kJ / (kg. C°)

But;

Heat gained by milk = Heat lost by hot chocolate

If the final temperature is x, then

Heat gained by milk

= 0.05 * 3.93 * (x-5)

= 0.1965x - 0.9825

Heat lost by hot chocolate;

= 0.2 * 3.751 * (95-x)

= 71.269 - 0.7502x

Therefore;

0.1965x - 0.9825 = 71.269 - 0.7502x

0.1965 x + 0.7502x = 71.269 + 0.9825

0.9467 x = 72.2515

x = 76.319 °C

Approximately, the new temperature is 76.3°C