Question

One gram of ice at $0^{0}C$ is added to $5$ grams of water at ${10}^{0}C$. If the latent heat of ice be $80$ cal/g, then the final temperature of the mixture is :

• A. $5^{0}C$
• B. $0^{0}C$
• C. $-5^{0}C$
• D. ${20}^{0}C$

Answer 1

The correct option is B $0^{0}C$

Ice converts to water only when the heat supplied is equal to the latent heat of ice
Latent heat$=m\times L_i=1\times 80=80cal$
Let's assume that water goes down to $0^o$C
Heat lost$=mc\Delta T=5\left(1\right)(10-0)=50cal$
Since the heat lost by the water is less than the latent heat required, the mixture of ice and water will stay at $0^o$C.