Question 1: Thermodynamics & KTG

Question

A piece of ice (heat capacity = 2100 J kg
-1
o
C
-1
and latent heat = 3.36 $ 	imes $ 10
5
J kg
-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

Accepted Answer

In the final state, ice-water mixture is in equilibrium. Thus, the temperature of m grams of ice is raised from $-$5 $^\circ$C to 0 $^\circ$C. The heat absorbed in this process is
Q
1
= mS$\Delta$T. ...... (1)
The state of m
1
= 1 g of ice is changed from solid to liquid. The heat absorbed in the melting process is
Q
2
= m
1
L. ........ (2)
The heat supplied is Q = 420 J. By energy conservation, Q = Q
1
+ Q
2
. Substitute Q
1
and Q
2
from equations (1) and (2) to get
$m = {{Q - {m_1}L} \over {S\Delta T}} = {{420 - ({{10}^{ - 3}})(3.36 	imes {{10}^5})} \over {(2100)(5)}}$
$ = 8 	imes {10^{ - 3}}$ kg = 8 g.

Thermodynamics & KTG

Integer / Numeric Answer Type