Question

A metal of mass $250\text{g}$ is kept at its melting point ${300}^{\circ }\text{C}$. It freezes at the same temperature releasing about $45\text{kJ}$ of energy. Find the specific latent heat of the metal in its S.I. unit.

• A. $180{\text{J kg}}^{-1}$
• B. $180{\text{J g}}^{-1}$
• C. $180{\text{kJ kg}}^{-1}$
• D. $180{\text{kJ g}}^{-1}$

Answer 1

The correct option is C $180{\text{kJ kg}}^{-1}$

Given:
The mass of the metal, $\text{m}=250\text{g}$
Latent heat, $\text{Q}=45\text{kJ}=45,000\text{J}$
Specific latent heat of the metal is given by,
$\text{L}=\frac{\text{Q}}{\text{m}}=\frac{45000}{250}=180{\text{J g}}^{-1}$

${\text{J kg}}^{-1}$ is the S.I. unit of specific latent heat.
$⟹1\text{kg}=1000\text{g}$ or $1\text{g}={10}^{-3}\text{kg}$

$180{\text{J g}}^{-1}=\frac{180}{{10}^{-3}}{\text{J kg}}^{-1}$
$=180\times {10}^3{\text{J kg}}^{-1}=180{\text{kJ kg}}^{-1}$