A molten metal of mass 150 g is kept at it's melting point 800° C. When it is allowed to freeze at the same temperature, it gives out 75,000 J of heat energy.

(a) What is the specific latent heat of the metal?

(b) If the specific heat capacity of metal is 200 J kg^-1 K^-1, how much additional heat energy will the metal give out in cooling to - 50° C?

(a) Given,

Mass (m) = 150 g

Heat energy given out (Q) = 75,000 J

Specific latent heat of the metal = ?

From relation Q = m x L

Substituting the values in the formula we get,

$75000 = 150 \times L \\[0.5em] \Rightarrow L = \dfrac{75000}{150} \\[0.5em] \Rightarrow L = 500 \text{ J g}^{-1} \\[0.5em]$

Hence, the specific latent heat of the metal = 500 J g^-1

(b) Specific heat capacity of metal is 200 J kg^-1 K^-1

Change in temperature
= 800 – (-50) = 800 + 50 = 850° C = 850 K

From relation,

Q = m x c x change in temperature

Substituting the values we get,

$Q = 0.15 \times 200 \times 850 \\[0.5em] Q = 25,500 J \\[0.5em]$

Hence, 25,500 J of heat energy will be given out