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Questions based on phase change

Question

A metal piece weighing 15 g is heated to $100^{0} C$ and then immersed in a mixture of ice and water at the thermal equilibrium. The volume of the mixture is found to be reduced by 0.15 ${cm}^{3}$ with the temperature of mixture remaining constant. Find the specific heat of the metal. Given specific gravity of ice = 0.92, specific gravity of water at $0^{0} C = 1.0, latent heat of fusion of ice = 80 cal - g^{- 1}$

Difficult

A

0.092 $cal / {gm}^{0} C$
B

0.124 $cal / {gm}^{0} C$
C

0.162 $cal / {gm}^{0} C$
D

0.242 $cal / {gm}^{0} C$

Solution

$\frac{m}{ρ_{ice}} - \frac{m}{ρ_{H_{2} o}} = 0.15$
m = $\frac{0.15 \times 0.92}{0.08}$
$∴ H_{lost} = H_{gained} \Rightarrow 15 \times S \times 100 = \frac{0.15 \times 0.92}{0.08} \times 80$
S = $0.092 cal / {gm}^{0} C$

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