A piece of ice (heat capacity $= 2100 J k g^{- 1}$ $^{o} C^{- 1}$ and latent heat $= 3.36 \times 10^{5} J k g^{- 1}$ ) of mass $m$ grams is at $- 5^{o} C$ at atmospheric pressure. It is given 420 $J$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

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Solution

The correct option is D 8
Heat $=$ latent heat $+$ Heat required to raise temp
$Q = m L + m C_{p} Δ T$
$420 = (m \times 2100 \times 5 + 1 \times 3.36 \times 10^{5}) \times 10^{- 3}$ where $m$ is in gm.
$m = 8 g$

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Similar questions

A 5 g piece of ice at $- 20^{\circ} C$ is put into 10 g of water at $30^{\circ} C$ . Assuming that heat is exchanged only between the ice and the water, find the final temperature of the mixture. Specific heat capacity of ice = $2100 J k g^{- 1}$ $^{\circ} C^{- 1}$ , specific heat capacity of water = $4200 J k g^{- 1}$ $^{\circ} C^{- 1}$ and latent heat of fusion of ice = $3.36 \times 10^{5} J k g^{- 1}$ .

Q. A 5g piece of ice at

- 20^{\circ}

C is put into 10g of water at

30^{\circ}

C. Assuming that heat is enchanged only between the ice and the water, find the final temperature of the mixture. Specific heat capacity of ice

= 2100 J k g^{- 1}^{\circ} C^{- 1}

. Specific heat capacity of water

= 4200 J k g^{- 1}^{\circ} C^{- 1}

and latent heat of fusion of ice

3.36 \times 10^{5} J k g^{- 1}

A 5 g piece of ice at $- 20^{\circ}$ C is put into 10 g of water at $30^{\circ}$ C. Assuming that heat is exchanged only between the ice and the water. Then find the heat required for phase change. Specific heat capacity of ice $= 2100 J k g^{- 1}^{\circ} C^{- 1}$ . Specific heat capacity of water $= 4200 J k g^{- 1}^{\circ} C^{- 1}$ and latent heat of fusion of ice $3.36 \times 10^{5} J k g^{- 1}$ .