This worked example problem demonstrates how to calculate the specific heat of a substance when given the amount of energy used to change the substance's temperature.

## Specific Heat Equation and Definition

First, let's review what specific heat is and the equation you'll use to find it. Specific heat is defined as the amount of heat per unit mass needed to increase the temperature by one degree Celsius (or by 1 Kelvin). Usually, the lowercase letter "c" is used to denote specific heat. The equation is written:

Q = mcΔT (you can remember this by thinking "em-cat")

where Q is the heat that is added, c is specific heat, m is mass, and ΔT is the change in temperature. The usual units used for quantities in this equation are degrees Celsius for temperature (sometimes Kelvin), grams for mass, and specific heat reported in calorie/gram °C, joule/gram °C, or joule/gram K. You can also think of specific heat as heat capacity per mass basis of a material.

There are published tables of molar specific heats of many materials. Note that the specific heat equation does not apply for phase changes. This is because the temperature does not change. When working a problem, you'll either be given the specific heat values and asked to find one of the other values, or else asked to find specific heat.

## Specific Heat Problem

It takes 487.5 J to heat 25 grams of copper from 25 °C to 75 °C. What is the specific heat in Joules/g·°C?**Solution:**

Use the formula

q = mcΔT

where

q = heat energy

m = mass

c = specific heat

ΔT = change in temperature

Putting the numbers into the equation yields:

487.5 J = (25 g)c(75 °C - 25 °C)

487.5 J = (25 g)c(50 °C)

Solve for c:

c = 487.5 J/(25g)(50 °C)

c = 0.39 J/g·°C

**Answer:**

The specific heat of copper is 0.39 J/g·°C.