Heat capacity measures the amount of energy that needs to be added to an object to make it one degree warmer. The heat capacity of an object is found using a simple formula – by dividing the amount of heat energy supplied by the change in temperature to determine the amount of energy required per degree. Every material in this world has a different heat capacity. (Source: Class 10 Standard Physics book)
Formula: Heat Capacity = (Given Heat Energy) / (Increase in Temperature)
Step
Method 1 of 2: Calculating the Heat Capacity of an Object
Step 1. Know the formula for heat capacity
The heat capacity of an object can be calculated by dividing the amount of heat energy supplied (E) by the change in temperature (T). The equation is: Heat capacity = E/T.
- Example: The energy required to heat a block to 5 degrees Celsius is 2000 Joules -- what is the heat capacity of the block?
- Heat capacity = E/T
- Heat capacity = 2000 Joule / 5˚C
- Heat capacity = 400 Joules per degree Celsius (J/˚C)
Step 2. Look for the temperature change
For example, if I want to know the heat capacity of a block, and I know it takes 60 Joules to raise the temperature of the block from 8 degrees to 20 degrees, I need to know the difference between the two temperatures to obtain the heat capacity. Since 20 - 8 = 12, the temperature of the block changes by 12 degrees. Therefore:
- Heat capacity = E/T
- Heat capacity of the block = 60 Joules / (20˚C - 8˚C)
- 60 Joule / 12˚C
- Heat capacity of the block = 5 J/˚C
Step 3. Add the correct units to your answer to give it meaning
A heat capacity of 300 means nothing if you don't know how it's measured. Heat capacity is measured by the energy required per degree. So, if we measure energy in Joules, and temperature change in Celsius, the final answer would be “how many Joules are needed per degree Celsius. Therefore, we will present our answer as 300 J/˚C, or 300 Joules per degree Celsius.
If you measure heat energy in calories and temperature in Kelvin, your final answer is 300 Cal/K
Step 4. Know that this equation works for objects that are cooling as well
When an object becomes two degrees colder, it loses exactly the same amount of heat as it would take to become 2 degrees warmer. Thus, if you ask, "What is the heat capacity of an object if it loses 50 Joules of energy and its temperature drops by 5 degrees Celsius," you can still use this equation:
- Heat capacity: 50 J/ 5˚C
- Heat capacity = 10 J/˚C
Method 2 of 2: Using the Specific Heat of Matter
Step 1. Know that specific heat refers to the energy required to raise the temperature of one gram of an object by one degree
When you look for the heat capacity of a unit of matter (1 gram, 1 ounce, 1 kilogram, etc.), you have looked for the specific heat of this object. Specific heat indicates the amount of energy required to raise the temperature of each unit of an object by one degree. For example, to raise the temperature of 1 gram of water by 1 degree Celsius requires 0.417 Joule of energy. So, the specific heat of water is 0.417 J/˚C per gram.
The specific heat of a material is constant. This means that all pure water has the same specific heat, which is 0.417 J/˚C
Step 2. Use the heat capacity formula to find the specific heat of a material
Finding specific heat is easy, that is, divide the final answer by the mass of the object. The results show how much energy is required for each piece of object, such as the number of joules needed to change the temperature of just one gram of ice.
- Example: "I have 100 grams of ice. To raise the temperature of the ice by 2 degrees Celsius it takes 406 Joules -- what is the specific heat of ice?"'
- Heat Capacity for 100 g Ice = 406 J/ 2˚C
- Heat Capacity for 100 g Ice = 203 J/˚C
- Heat Capacity for 1 g Ice = 2.03 J/˚C per gram
- If you're confused, think about it this way -- to raise the temperature by one degree for every gram of ice it takes 2.03 Joules. So, if we have 100 grams of ice, we need 100 times more Joules to heat it all up.
Step 3. Use specific heat to find the energy required to raise the temperature of the material to any temperature
The specific heat of matter indicates the amount of energy required to raise the temperature of one unit of matter (usually 1 gram) by one degree. To find the heat required to raise the temperature of any object to any temperature, we simply multiply all the parts. Energy Required = Mass x Specific Heat x Change in Temperature. The answer is always in units of energy, such as Joules.
- Example: "If the specific heat of aluminum is 0.902 Joules per gram, how many Joules are needed to raise the temperature of 5 grams of aluminum by 2 degrees Celsius?
- Energy Required = 5 g x 0.902 J/g˚C x 2˚C
- Energy Required = 9.02 J
Step 4. Know the specific heats of common materials
To help practice, study common specific heats, which you can see on an exam or appear in real life. What can you learn from this? For example, note that the specific heat of metal is much lower than that of wood -- this is the reason why metal spoons heat up faster than wood if left in a cup of hot chocolate. A lower specific heat means an object heats up faster.
- Water: 4, 179 J/g˚C
- Air: 1.01 J/g˚C
- Wood: 1.76 J/g˚C
- Aluminum: 0.902 J/g˚C
- Gold: 0.129 J/g˚C
- Iron: 0.450 J/g˚C
Tips
- The International (SI) unit of heat capacity is Joules per Kelvin, not just Joules
- The change in temperature is represented by a temperature unit delta instead of just a temperature unit (say: 30 Delta K instead of just 30K)
- Energy (heat) must be in Joules (SI) [Recommended]
