A metal ball of mass $400 g$ and at $600^{\circ} C$ is placed on a block of ice when $428 g$ of ice melts. If the specific heat capacity of the metal ball is $0.6 J {g^{- 1}}^{\circ} C^{- 1}$ , calculate the specific latent heat of ice.

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Solution

Step 1: Given data
The mass of a metal ball is $400 g$ and placed on a block of ice when $428 g$ of ice melts.
And the sp. heat capacity of the metal ball is $0.6 J {g^{- 1}}^{\circ} C^{- 1}$ .
Step 2: Calculating the heat gained by ice to melt
Let the specific latent heat of ice is $L J {g^{- 1}}^{\circ} C^{- 1}$
The amount of heat required to melt the ice is
$= m a s s o f i c e \times s p e c i f i c l a t e n t h e a t o f i c e = 428 \times L$
Step 3: Calculating the Heat lost by the metal ball
The heat lost by the ball
$m a s s o f m e t a l b a l l \times s p e c i f i c h e a t c a p a c i t y o f b a l l \times t e m p e r a t u r e d i f f e r e n c e = 400 \times 0.6 \times (600 - 0) J u l e = 144000 J u l e$
Step 4: Calculating the sp. latent heat of ice
The main theorem of calorimetry
$h e a t g a i n = h e a t l o s t \Rightarrow 428 \times L = 144000 \Rightarrow L = \frac{144000}{428} \Rightarrow L = 336.4 J g^{- 1}$
Hence, the specific latent heat of ice is $336.4 J g^{- 1}$ .

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Q. 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.

2 k g

of ice melts when water at

100^{\circ} C

is poured in a hole drilled in a block of ice. What mass of water was used?

Given: specific heat capacity of water =

4200 J k g^{- 1} K^{- 1}

specific latent heat of ice =

336 \times 10^{3} J k g^{- 1}

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A metal ball of mass 400g and at 600∘C is placed on a block of ice when 428g of ice melts. If the specific heat capacity of the metal ball is 0.6Jg-1∘C-1, calculate the specific latent heat of ice.

A metal ball of mass $400 g$ and at $600^{\circ} C$ is placed on a block of ice when $428 g$ of ice melts. If the specific heat capacity of the metal ball is $0.6 J {g^{- 1}}^{\circ} C^{- 1}$ , calculate the specific latent heat of ice.