Final answer:
To raise the temperature of a 5.0-gram sample of water by 15.0 degrees Celsius, it takes 75 calories of heat. This is calculated using the formula q = m × ΔT × C, with C being 1 cal/g°C for water.
Step-by-step explanation:
To calculate the amount of heat needed to raise the temperature of a 5.0-gram sample of water by 15.0 degrees Celsius, we use the fact that the calory is the unit of energy required to raise the temperature of 1 gram of water by 1 degree Celsius. Since we are dealing with water, the specific heat capacity is typically used, which is 4.184 J/g °C. However, since the question asks for calories, we will stick with the calorie unit.
The formula to determine the heat energy required is:
q = m × ΔT × C
where q is the heat in calories, m is the mass in grams, ΔT is the change in temperature in degrees Celsius, and C is the specific heat capacity in calories per gram per degree Celsius (1 cal/g°C for water). For this question:
q = 5.0 g × 15.0 °C × 1 cal/g°C
Therefore:
q = 75 cal
It takes 75 calories of heat to raise the temperature of a 5.0-gram sample of water by 15.0 degrees Celsius.