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# Heat capacity: Converting between heat and change in temperature

How can we measure heat? Here are some things we know about heat so far:

• When a system absorbs or loses heat, the average kinetic energy of the molecules will change. Thus, heat transfer results in a change in the system’s temperature as long as the system is not undergoing a phase change.
• The change in temperature resulting from heat transferred to or from a system depends on how many molecules are in the system.

We can use a thermometer to measure the change in a system’s temperature. How can we use the change in temperature to calculate the heat transferred?In order to figure out how the heat transferred to a system will change the temperature of the system, we need to know at least 222 things:

• The number of molecules in the system
• The heat capacity of the system

The heat capacity tells us how much energy is needed to change the temperature of a given substance assuming that no phase changes are occurring. There are two main ways that heat capacity is reported. The specific heat capacity (also called specific heat), represented by the symbol  c, or C start text, C, end text, is how much energy is needed to increase the temperature of one gram of a substance by 1∘ or 1K.

Specific heat capacity usually has units of  J/grams.K The molar heat capacity,

Cm​start text, C, end text, start subscript, start text, m, end text, end subscript or \text C_{\text{mol}}Cmol​start text, Cm, Cmol, measures the amount of thermal energy it takes to raise the temperature of one mole of a substance by 1 ∘C1,  or 1 K, and it usually has units of J / mol.K

For example, the heat capacity of lead might be given as the specific heat capacity, 0.129 j/g.K or the molar heat capacity, 26.65 J/ mol.K