Specific Heat Capacity - Learn

Specific Heat Capacity

When a substance is heated, its temperature will rise. The amount of thermal energy a substance absorbs will be proportional to the rise in temperature. For any substance, the rise in temperature will also be proportional to the mass of the substance and the type or nature of the substance.

The heat capacity of a substance is the ratio of the amount of heat required for a given change in temperature. This is a physical property of any substance and is related to the structure of the substance. A more useful quantity is the specific heat capacity of a substance. The specific heat capacity of any substance is the amount of energy required to raise the temperature of 1kg of the substance by 1ºC, without a phase change.

The specific heat capacity of a substance is useful for determining how much energy is required to change the temperature of that substance:

$Q=mc\Delta T$

where:

$Q$ is the heat energy transferred (in J)

$m$ is the mass of the substance (in kg)

$c$ is the specific heat capacity of the substance (in Jkg^-1K^-1)

$\Delta T$ is the change in temperature (in ºC or K)

Different substances have different specific heat capacities and the correct value should be used depending on the problem considered. Water is a common substance that is used in many problems. Water has a specific heat capacity of 4200 Jkg^-1K^-1. Some other values are:

air = 1000 Jkg^-1K^-1
glass = 840 Jkg^-1K^-1
copper = 390 Jkg^-1K^-1
mercury = 140 Jkg^-1K^-1

Notice the values for metals are lower than water. This means less energy is required to heat equal masses of metals when compared to water by the same temperature.

Example 1:

Calculate the energy required to heat 500mL of water from 25ºC to 70ºC:

Answer:

note: we assume the density of water is 1gm/mL

$m$ = 500gm = 0.5kg

$c$ of water = 4200 Jkg^-1K^-1

$\Delta T$ = 70-25 = 45ºC

using: $Q=mc\Delta T$

$Q=0.5\times 4200\times (45)$

$Q=94500\;J$

$Q=94.5\;kJ$