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Standard XII

Physics

Specific Heat Capacity

A metal ball ...

Question

A metal ball of mass 400 g and at $600^{o} C$ is placed on the block of ice melting 428 g of ice. If the sp. heat capacity of metal ball is $0.6 J g^{- 1}^{o} C^{- 1}$ . Calculate sp. latent heat of ice.

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Solution

As the block does not melt completely, therefore, final temperature is zero degree Celsius.
For Ice:
$M a s s = 428 g$
$S . H . C . / S . L . H . = ? (L)$
$I n i t i a l T e m p . = 0^{o} C$
$F i n a l T e m p . = ∴ θ_{R} = 0^{o} C$
for Metal ball:
$M a s s = 400 g$
$S . H . C . / S . L . H . = 0.6 J g^{- 1}^{o} C^{- 1}$
$I n i t i a l T e m p . = 600^{o} C$
$F i n a l T e m p . = ∴ θ_{F} = (600 - 0)$
$= 600^{o} C$
$H e a t g a i n e d b y i c e t o m e l t = m L_{i c e}$
$= 428 g \times L$
$H e a t l o s t b y m e t a l b a l l = m c θ_{F}$
$= 400 \times 0.6 \times 600$
$= 144000 J .$
$H e a t g a i n e d = H e a t l o s t$
$= 428 g \times L = 144000 J .$
$L = \frac{144000}{428} = 336.4 J g^{- 1}$

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A metal ball of mass 400 g and at 600oC is placed on the block of ice melting 428 g of ice. If the sp. heat capacity of metal ball is 0.6Jg−1oC−1. Calculate sp. latent heat of ice.

A metal ball of mass 400 g and at $600^{o} C$ is placed on the block of ice melting 428 g of ice. If the sp. heat capacity of metal ball is $0.6 J g^{- 1}^{o} C^{- 1}$ . Calculate sp. latent heat of ice.