Thermal Physics

5.1.1 Temperature

Temperature shows how hot an object is! 

If two object are in contact and have different temperatures, there will be a transfer of heat energy between them (from the hotter to colder!).

Thermal Equilibrium: when there is no net flow of thermal energy between two objects, i.e. they have the same temperature.

Absolute temperature (thermodynamic temperature): measured in Kelvin (^oK) and does not depend on any properties of substances, unlike the Celsius (^oC) that is defined on freezing point (0^oC) and boiling point (100^oC) of water, which is dependent on pressure and hence not always accurate. 

Kelvin is always positive -> the lowest is zero (we call it absolute zero).

5.1.2 Solid Liquid and Gas

Kinetic Model: substances are made of particles (atoms or molecules), and they have kinetic energy!

Solid: particles have strong bond, regularly arranged, packed closely, they can just vibrate in their fixed positions.

Liquid: particles are strongly bonded (but less that solid), particles can slide over each other.

Gas: particles are free to move! They are further apart than both solid, almost no bonding force between them, and they move randomly. This random motion is called Brownian motion! The collision between gas particles is assumed to be elastic (KE is conserved).

Most substances are denser in solid state than in liquid or gas, an example of exception is water!

Internal energy is the sum of the KE and PE of material.

KE changes when temperature changes. It is due to movement of particles.

PE changes when there is a change of state. It is due to electrostatic bond between particles. 

Temperature does not change during change of state (KE does not change). 

Graph below shows heating at constant rate. 

5.1.3 Thermal properties of materials

5.1.3.1 Specific Heat Capacity: 

Specific Heat Capacity is the amount of energy needed to change the temperature of 1 kg of material by 1 degrees (either ^oC or ^oK).

Determining the specific heat capacity:

Equipment needed for a solid and a liquid

An example of the experiment setup is shown below. 

Link for thermometer.

Energy needed to raise the temperature from the electric heater is given by:

Then the specific heat capacity is calculated by:

Using the gradient of the line above, we can derive the following relationship:

Method of mixtures:

To determine the specific heat capacity of a substance we mix it with another substance that we its specific heat capacity. Initially they are at different temperatures, we measure their masses and measure their final temperature when they reach thermal equilibrium.

Procedure:

1. Heat the Metal Block: Place the metal block, of known mass of m_m, in boiling water until it reaches a known temperature T_m​ (usually around 100°C if boiling water is used).  
2. Prepare the Water: Measure a known mass of water m_w ​ in a calorimeter or insulated container. Record the initial temperature of the water T_w​.
3. Mix the Metal and Water: Quickly transfer the hot metal block into the water. Stir gently to ensure uniform temperature.
4. Record the Final Temperature: Wait until the temperature stabilizes, and then record the final equilibrium temperature T_f of the water and metal block.

Calculations:

According to the method of mixtures, the heat energy lost by the metal block will be equal to the heat energy gained by the water:

Example Values:

Let’s assume:

• Mass of metal block, m_m = 0.5 kg
• Mass of water, m_w = 0.2 kg
• Specific heat capacity of water, c_w = 4,186 J/kg°C
• Initial temperature of metal block, T_m=100°C
• Initial temperature of water, T_w=25°C
• Final temperature, T_f=30°C

Plugging in the values: