In order to figure out the amount of heat required to change the temperature of a substance you need to know three things.
- mass of the substance
- the specific heat capacity of the substance
- the temperature change needed or wanted
Once you know these three things, you can find the amount of energy required to change that substance's temperature by a set amount. Knowing that the units of specific heat capacity are Joules per kilogram degree Celsius, you can simply multiply the specific heat capacity by the mass and the change in temperature required.
Heat Required
\(\mathsf{ Q = mc \Delta T }\)
...where Q is the heat required, m is the mass of the substance in kilograms, c is the specific heat capacity in Joules per kilogram-degree Celsius, and ΔT is the change in temperature.
Keep in mind that the change in temperature can be positive (increasing) or negative (decreasing). The result is either a positive heat value, which means heat is given to the substance, or a negative heat value, which means the substance is transferring heat to something else.
Question
How much heat must be added to increase the temperature of a 0.789 kg piece of silver from 25.0°C to 78.0°C? (csilver = 239 J/kg°C)
Use \(\mathsf{ Q = mc \Delta T }\) to solve for Q.
\(\mathsf{ Q = (0.789 \text{ kg})(239 \text{ J/kg°C})(78 \text{°C} - 25 \text{°C}) }\)
\(\mathsf{ Q = 1.00 \times 10^3 \text{ J} }\)
