To calculate the heat needed to melt the ice and raise the temperature, we need to break it down into two steps:
Step 1: Heat needed to melt the ice
The mass of ice is 0.32 kg, and the latent heat of ice to water is 80 cal/g. Therefore, the heat needed to melt the ice is:
0.32 kg x 80 cal/g = 25.6 kcal
Step 2: Heat needed to raise the temperature from 0°C to 25°C
The specific heat of water is 1 cal/g.°C, and the mass of water produced by melting the ice is also 0.32 kg. Therefore, the heat needed to raise the temperature from 0°C to 25°C is:
0.32 kg x 25°C x 1 cal/g.°C = 8 kcal
Total heat needed = Heat needed to melt the ice + Heat needed to raise the temperature
Total heat needed = 25.6 kcal + 8 kcal = 33.6 kcal
Therefore, 33.6 kilocalories of heat would be needed to melt 0.32 kg of ice at 0°C and increase the temperature to 25°C.