Question

A metal ball of $0.20\mathrm{kg}$ and at $200°C$ when placed on an ice block melts $100\mathrm{g}$ of ice when its temperature stops falling. If specific latent heat of ice is $340{\mathrm{Jg}}^{-1}$. Calculate the specific heat capacity of the metal ball.

Answer 1

Step 1: Given data

1. The mass of the metal ball is $0.20\mathrm{kg}$
2. Mass of ice block melted is $100\mathrm{g}$ and let specific latent heat of ice is $340{\mathrm{Jg}}^{-1}$

Step 2: Finding the specific heat capacity of the metal ball

Let specific heat Capacity of solid ball $=c$

Heat lost by hot ball

$$\begin{gathered} =Mc(T-0) \\ =(0.20\times 1000)\times c(200-0) \\ =200\times 200c \end{gathered}$$

Heat gained by the ice

$$\begin{gathered} =m\mathrm{L} \\ =100\times 340 \end{gathered}$$

Now, by the principle of calorimetry,

Heat lost by hot ball = Heat gained by the ice

$$\begin{gathered} 200\times 200c=100\times 340 \\ c=\frac{34000}{2\times 20000} \\ c=0.85J{g}^{-1}°C^{-1} \end{gathered}$$

Hence, the specific heat capacity of a metal ball is $0.85J{g}^{-1}°C^{-1}$.