Heat Energy

To determine the amount of heat energy possessed by a body, three key factors are considered:

• Change in temperature (θ)
• Specific heat capacity of the body (C)
• Mass of the body (m)

The quantity of heat (Q) is given by the equation:

$$ Q = mcΔθ $$

Heat energy is measured in Joules (J).

Heat Capacity

Heat capacity is the amount of heat required to raise the temperature of a substance by one degree. It is measured in Joules per Kelvin (J/K).

Mathematically, it is expressed as:

Heat capacity = Mass × Specific heat capacity

$$ C = mc $$

Specific Heat Capacity

The specific heat capacity of a substance is the heat required to raise the temperature of one unit mass of the substance by one degree.

The amount of heat energy received by a body depends on:

• Mass of the body (m)
• Temperature change (θ₂ - θ₁)
• The nature of the material

The formula for heat energy is:

$$ Q = mcΔθ $$

Or, in expanded form:

$$ Q = mc(θ_2 - θ_1) $$

Determining Specific Heat Capacity

The specific heat capacity (C) is a proportionality constant that depends on the nature of the substance. It is given by:

$$ C = \frac{Q}{m(θ_2 - θ_1)} $$

The unit of specific heat capacity is J/gK.

Methods for Determining Specific Heat Capacity

• The method of mixtures
• The electrical method

Determination of Specific Heat Capacity by the Mixture Method

To determine the specific heat capacity of a solid lead block using the mixture method, follow these steps:

• The lead block is weighed on a balance, and its mass is recorded as M_s.
• A lagged calorimeter is dried and weighed, with its mass recorded as M_c.
• The calorimeter is then partially filled with water and reweighed, with the new mass recorded as M_cw.
• The initial temperature of the water is recorded as θ₁.
• The lead block is suspended in boiling water at a temperature of θ₂ and then transferred to the calorimeter.
• The mixture is stirred to ensure a uniform final temperature, recorded as θ₃.

Heat Energy Balance

Using the principle of heat exchange:

Heat lost by the lead = Heat gained by the calorimeter and water

Given:

• \( C_s \) = Specific heat capacity of lead
• \( C_c \) = Specific heat capacity of the calorimeter
• \( C_w \) = Specific heat capacity of water

The heat balance equation is:

Rearranging to solve for \( C_s \):

This equation allows the calculation of the specific heat capacity of lead based on experimental data.

Determining the Specific Heat Capacity of a Solid

To calculate the specific heat capacity (C_b) of a solid brass block, the following setup is used:

• Two holes are made in a weighed brass block.
• A thermometer and a heating element connected to a power source are inserted into the holes.
• Oil is poured into the holes to improve thermal conductivity.

Assuming no heat is lost to the surroundings, the total electrical heat energy supplied by the heating coil is equal to the heat energy absorbed by the brass block.

Heat energy supplied by the coil = Heat energy gained by the brass

\( IVt = M C_b \Delta \theta \)

Where:

• \( I \) = Current (A)
• \( V \) = Voltage (V)
• \( t \) = Time (s)

Applying Ohm's Law

From Ohm’s law:

\( V = IR \)

Substituting into the heat equation:

\( I^2 R t = M C_b \Delta \theta \)

Rearranging:

\( I^2 t R = M C_b \Delta \theta \)

Determining the Specific Heat Capacity of a Liquid

For a liquid, the total heat energy supplied by the coil is equal to the sum of the heat energy gained by the liquid and the heat energy gained by the calorimeter.

Heat energy supplied by the coil = Heat energy gained by the liquid + Heat energy gained by the calorimeter

\( IVt = M_l C_l \Delta \theta + M_c C_c \Delta \theta \)

Where:

• \( M_l \) = Mass of the liquid (g)
• \( C_l \) = Specific heat capacity of the liquid (J/gK)
• \( M_c \) = Mass of the calorimeter (g)
• \( C_c \) = Specific heat capacity of the calorimeter (J/gK)