A piece of ice (heat capacity=2100JK$g^{- 1}$ $℃^{- 1}$ and latent heat=${3.36 imes 10}^{5}$ ${Jkg}^{- 1}$) of mass $m$ gram is at $- 5℃$ 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 g of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

Question

A piece of ice (heat capacity=2100JK$g^{- 1}$ $℃^{- 1}$ and latent heat=${3.36 	imes 10}^{5}$ ${Jkg}^{- 1}$) of mass $m$ gram is at $- 5℃$ 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 g of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

Dr. Abubacker · Accepted Answer

(a) Language of question is slightly wrong. As heat capacity and specific heat are two different physical quantities. Unit of heat capacity is $\ Jkg^{- 1}$, not $Jkg^{- 1}℃^{- 1}$. The heat capacity given in the question is really the specific heat. Now applying the heat exchange equation:
$420 = \left( m 	imes 10^{- 3} ight)(2100)(5) + \left( 1 	imes 10^{- 3} ight)(3.36 	imes 10^{5})$
Solving this equation, we get
$m$=8g
$	herefore$ The correct answer is 8.

Explanation

Reviewed by Dr. Abubacker

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