Specific Heat Capacity and Thermal Physics

Energy Transfer and Temperature Change

Thermal energy can be transferred to or from an object through three primary processes: conduction, convection, and radiation. In many physical scenarios, more than one of these processes occurs simultaneously. The resulting change in an object's temperature is determined by the net heat transfer, which is the difference between the total energy transferred into the object and the total energy transferred out of it.

When there is a net transfer of heat into an object, its temperature typically increases. On a microscopic level, this causes the particles that make up the object to move more energetically, increasing their kinetic energy. Conversely, when more heat is transferred from an object than to it, its temperature decreases and its particles move less energetically. It is important to note that these temperature changes occur provided the object is not currently undergoing a change of state, such as melting or boiling.

If an object is not changing state, the magnitude of its temperature change depends on two main factors: the mass of the object and the specific type of material it is composed of.

Heat Capacity and Specific Heat Capacity

To quantify these thermal changes, we distinguish between the property of a specific object and the property of the substance itself.

1. Heat Capacity: This is the thermal energy transferred per unit change in temperature of a particular object or sample. It is measured in $J ^\circ C^{-1}$.
2. Specific Heat Capacity: In physics, the term specific refers to a property per unit mass. Therefore, the specific heat capacity ($c$) is the heat capacity per unit mass of a substance. This is a characteristic property of the material rather than the specific object.

Specific heat capacity is measured in J kg^{-1} ^\circ C^{-1}. It can be calculated by measuring the temperature change of a sample with a known mass when a measured amount of thermal energy is transferred.

The Specific Heat Capacity Formula

The relationship between thermal energy, mass, specific heat capacity, and temperature change is given by the formula:

$specific\ heat\ capacity = \frac{thermal\ energy}{mass \times temperature\ change}$

In this equation, energy is measured in Joules ($J$), mass is measured in kilograms ($kg$), and temperature change is measured in degrees Celsius ($^\circ C$).

Comparative Data for Substances

Different substances require different amounts of energy to change their temperature. The following table provides the specific heat capacities for common substances, rounded to two significant figures:

Substance	Specific heat capacity (J kg^{-1} ^\circ C^{-1})
lead (solid)	130
copper (solid)	390
aluminium (solid)	900
water (solid/ice)	2100
ethanol (liquid)	2400
water (liquid)	4200
hydrogen (gas)	14000

Worked Examples

Example 1: Calculating Specific Heat Capacity

Calculate the specific heat capacity of magnesium if a $3.0 kg$ sample increases in temperature by $15 ^\circ C$ when $45,000 J$ of thermal energy is transferred to it from the surroundings.

Using the formula: $c = \frac{\text{thermal energy}}{\text{mass} \times \text{temperature change}}$ $c = \frac{45000}{3 \times 15}$ c = 1000 J kg^{-1} ^\circ C^{-1}

Example 2: Calculating Energy Transfer

Calculate the energy transferred to the surroundings when an aluminium block with a mass of $2.0 kg$ decreases in temperature from $25.0 ^\circ C$ to $20.0 ^\circ C$. (The specific heat capacity of aluminium is 900 J kg^{-1} ^\circ C^{-1}.)

First, find the temperature change: $\Delta T = 25.0 ^\circ C - 20.0 ^\circ C = 5.0 ^\circ C$

Now, rearrange the formula to find the thermal energy: $\text{thermal energy} = c \times \text{mass} \times \text{temperature change}$ $\text{thermal energy} = 900 \times 2.0 \times 5.0$ $\text{thermal energy} = 9000 J$