Question

One gram of ice at $0^o$C is added to 5 gram of water at 10${}^o$C. Final temperature of the mixture is:

• A. -5${}^o$C
• B. 5${}^o$C
• C. 0${}^o$C
• D. None of these

Answer 1

The correct option is A -5${}^o$C

Given: One gram of ice at $0^{o}C$ is added to 5 gram of water at ${10}^{o}C$.

To find the final temperature of the mixture

Solution:

As per given condition,

Specific heat of water, $s_1=s_2=4.2J/g{/}^{\circ }C$

Latent heat of fusion of ice, $L=334J/g$

Mass of water, $m_1=5g$
Mass of ice, $m_2=1g$

Temperature of Water, $T_2={10}^{\circ }C$

Temperature of ice, $T_1=0^{\circ }C$

Let the final temperature be $T$

Ice could melt and become water. Water at $10°C$ will cool down.

First 1g ice melts and then its temperature increases by gaining heat from 5g water.

Heat lost by 5g water = Heat gained by 1g ice = heat energy for melting of 1g of ice + heat energy for increase of temperature of 1g water from 0°C to T°C

$m_1{s}_1(T_2-T)=m_{2}L+m_2{s}_2(T-T_1)⟹5\times 4.2(10-T)=1\times 334+1\times 4.2(T-0)⟹210-21T=334+4.2T⟹21T+4.2T=210-334⟹25.2T=-124⟹T=-{4.9}^{\circ }C$

Hence the final temperature of the mixture is $-5^{\circ }C$.