Final answer:
The heat capacity of 28.4 g of water is 118.8272 J/°C or 28.4 cal/°C, and the heat capacity of 45.8 g of nitrogen gas is 47.632 J/°C or 11.38 cal/°C.
Heat capacity is an extensive property indicating the total amount of heat needed to raise a substance's temperature by one degree, whereas specific heat capacity is an intensive property that applies to one gram of the substance.
Step-by-step explanation:
To calculate the heat capacity in joules and in calories per degree, we use the specific heat capacity of the substance and its mass.
For water, the specific heat capacity is about 4.184 J/g°C, and for nitrogen gas, it is approximately 1.04 J/g°C. Now let's calculate:
- (a) For 28.4 g of water: Heat capacity = mass × specific heat capacity = 28.4 g × 4.184 J/g°C = 118.8272 J/°C. To convert to calories, we use the conversion 1 cal = 4.184 J, which gives us 28.4 g × 1 cal/g°C = 28.4 cal/°C.
- (b) For 45.8 g of nitrogen gas: Heat capacity = 45.8 g × 1.04 J/g°C = 47.632 J/°C. To convert to calories, we use 1 cal = 4.184 J, so we get 45.8 g × (1.04/4.184) cal/g°C = 11.38 cal/°C.
It's worth noting that the heat capacity of a substance tells us how much heat energy is needed to raise the temperature of that entire sample by one degree Celsius, while specific heat capacity refers to the amount of heat needed to raise the temperature of one gram of the substance by one degree Celsius.