Question

One kg of ice at $0^{o}C$ is mixed with $1kg$ of water at ${10}^{o}C$. The resulting temperature will be

• A. between $0^{o}C$ and ${10}^o$C
• B. $0^{o}C$
• C. less than $0^{o}C$
• D. greater than $0^{o}C$

Answer 1

Answer: (B)

$0^{o}C$

Solution:

Specific heat of water is 1 cal/g. There is totally 1kg, so it possesses 1000cal of energy. Now, since ice is already at $0^{o}C$, it needs latent heat to turn into water. This energy is provided by the water. Latent heat of ice is 80cal/g. So, for 1kg, it requires 8000cal. But water only possess 1000cal of energy. So, only certain mass of ice will get converted into water at $0^{o}C$, and the rest of the water at ${10}^{o}C$ will cool down to $0^{o}C$ also. But, since only 1000cal is available, part of the ice remains as ice. So, temperature in the end is $0^{o}C$ .

Hence the correct option is B.