Question

I take 1.0 kg of ice and dump it into 1.0 kg of water and, when equilibrium is reached, I have 2.0 kg of ice at 0°C. The water was originally at 0°C.

The specific heat of water = 1.00 kcal/kg⋅°C, the specific heat of ice = 0.50 kcal/kg⋅°C, and the latent heat of fusion of water is 80 kcal/kg.

The original temperature of the ice was:
a. one or two degrees below 0°C.b. −80°C.c. −160°C.d. The whole experiment is impossible.

Answer 1

The original temperature of the ice was a. one or two degrees below 0°C.

Step-by-step explanation:

Heat transfer is the process by which thermal energy is exchanged between systems. It occurs through conduction, where heat moves through materials, convection, involving the movement of fluids, and radiation, which involves electromagnetic waves. Understanding heat transfer is essential in fields like physics, engineering, and environmental science.

To find the original temperature of the ice, we need to calculate the heat transferred during the process. First, we need to bring the ice up to 0°C and melt it. This requires a heat transfer of 4.74 kcal. This will lower the temperature of the water by 23.15°C. After the ice has melted and the system reaches equilibrium, the final temperature of the water is 20.6°C. Therefore, the original temperature of the ice was one or two degrees below 0°C.

Answer 2

.c. −160°C

Step-by-step explanation:

In the whole process one kg of water at 0°C loses heat to form one kg of ice and heat lost by them is taken up by ice at −160°C . Now see whether heat lost is equal to heat gained or not.

heat lost by 1 kg of water at 0°C

= mass x latent heat

= 1 x 80000 cals

= 80000 cals

heat gained by ice at −160°C to form ice at 0°C

= mass x specific heat of ice x rise in temperature

= 1 x .5 x 1000 x 160

= 80000 cals

so , heat lost = heat gained.