Question

A piece of metal of mass 50g is at ${{100}^{o}}$C. it is placed on the block of ice. Calculate the amount of ice melts, if the specific heat capacity of the metal is $0.8J{{g}^{-1}}{}^{0}{{C}^{-1}}$ and specific latent heat of the fusion of ice is$340J{{g}^{-1}}$.

Answer 1

It is given in the question that metal temperature is at ${{100}^{o}}$C. Which is placed on the ice, therefore melting can be stopped only when the temperature of the metal comes down at ${{0}^{o}}C$ and by using this temperature difference we can calculate heat loss or gain and by comparing two heat formulas we can get total mass of ice which is melt during this condition.
Formula used:
$\begin{aligned} & \Delta Q=mc\Delta T \\\ & \Delta Q=mL \\\ \end{aligned}$

Complete answer:
This question is based on the simple phenomena that heat loss by metal is equal to heat gained by the ice cube.
Now formula for the heat loss by the metal is,
$\Delta Q=mc\Delta T...\left( 1 \right)$
Where, $\Delta Q$ = heat loss by the metal
c = specific heat
$\Delta T=$Temperature difference
Now formula for ice that is gained heat from the metal
$\Delta Q=mL...\left( 2 \right)$
Where, $\Delta Q$ = heat gained by ice.
M = mass of the ice.
L = latent heat
Now equalizing equation (1) and the equation (2)
$mc\Delta T=ML....\left( 3 \right)$
Here mass of the metal is given as =m = 50g
Specific heat is given as = c = 0.8J/gc
Latent heat of the ice is given as=L = 340J/g
Here the total temperature difference will be ${{100}^{o}}$C, because ice will stop melting when metal reached temperature at ${{0}^{o}}C$
Therefore $\Delta T={{100}^{o}}C$
Now let’s substitute all the values in the equation (3)
$\begin{aligned} & \Rightarrow 50\times 0.8\times 100=M\times 340 \\\ & \Rightarrow M=\dfrac{50\times 0.8\times 100}{340} \\\ & \therefore M=11.76gram \\\ \end{aligned}$
Therefore 11.76g of mass will melt from the ice.

Note:
As an approach to solve this question first we write formula of heat loss from the metal and then we equalize this formula with the formula of the ice cube which is melting due to heat gain from the metal by equalizing this two formula we get total mass of ice which is melted which is 11.76g.