Question

An immersion heater of power $20W$ just keeps $200g$ of solid metal at its melting point. The heater is switched ON and temperature starts raising after $4min$, then the specific latent heat of fusion of the metal is ________.

• A. $24J{g}^{-1}$
• B. $24cal{g}^{-1}$
• C. $24calk{g}^{-1}$
• D. $24Jk{g}^{-1}$

Answer 1

The correct option is A

$24J{g}^{-1}$

Step 1: Analysing the given data:
Power of the heater $\left(P\right)=20W$
mass of metal $\left(m\right)=200g$
Time $\left(t\right)=4min=240s$
Find Latent heat of fusion $\left(L\right)$:

Step 2: Calculating the heat supplied by the heater:
Heat supplied by the heater is given by:
$Q=Pt$
$\Rightarrow Q=20\times 240$
$\Rightarrow Q=4800J$

Step 3: Calculating the Latent heat of fusion:
Latent heat of fusion of a substance is given by:
$L=\frac{Q}{m}$
$\Rightarrow L=\frac{4800}{200}$
$\Rightarrow L=24J{g}^{-1}$

Thus, Specific latent heat of fusion of the metal is $24J{g}^{-1}$.
Hence, Option (A) is the correct answer.