Question

A piece of ice (heat capacity `=2100 J kg^(-1) .^(@)C^(-1)` and latent heat `=3.36xx10^(5) J kg^(-1)`) of mass m grams is at `-5 .^(@)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 in gram is

Answer 1

Correct Answer - 8
Here, `s_(ice) =2100 J kg^(-1) .^(@)C^(-1)` ,
`L=3.36xx10^(5) J kg^(-1) , Q=420 J`
`theta_(1) =-5^(@)C, m_(ice) =1g =(1)/(1000)kg`
Let m kg ice be originally present. As per question
`ms_(ice)(0-theta_(1)) + m_(ice)L=Q`
`mxx2100[0-(-5)] + (1)/(1000)xx3.36xx10^(5) =4420`
or `mxx2100xx5 =420 - 336 =84`
or `m=(84)/(2100xx5)kg =(84xx1000)/(2100xx5)=8 g`