How many kilocalories of heat are needed to raise the temperature of 460 grams of water from 13 C to 45 C?

The specific heat capacity of water is 1 calorie/gram °C. To convert this to kilocalories, we divide by 1000, so 1kcal/kg°C. The temperature change is 45 - 13 = 32°C. Therefore, the heat required is 460g * 32°C * 1kcal/kg°C = 14720 kcal.