Topic 6.4 Notes – Heat Capacity and Calorimetry

1. Heat Transfer and Energy Conservation

Heat (q) is energy transferred because of a temperature difference.
It always flows from warmer → cooler until both reach the same temperature (thermal equilibrium).

• Units: J or kJ
• Heating → system energy increases
• Cooling → system energy decreases

Temperature change is:

$$\Delta T = T_{\text{final}} - T_{\text{initial}}$$

• If $\Delta T > 0$, temperature increased
• If $\Delta T < 0$, temperature decreased

The First Law of Thermodynamics

Energy is conserved. It cannot be created or destroyed.

In calorimetry, this becomes:

$$q_{\text{system}} + q_{\text{surroundings}} = 0$$

or

$$q_{\text{lost}} = -q_{\text{gained}}$$

If something loses 250 J, something else must gain 250 J. On tests, this idea is huge. If you forget it, everything falls apart.

Chemical systems change energy in three ways:

1. Heating or cooling
2. Phase changes
3. Chemical reactions

This topic focuses on heating/cooling measured with calorimetry.

2. The Heat Transfer Equation

When temperature changes without a phase change, use:

$$q = mc\Delta T$$

• $q$ = heat (J)
• $m$ = mass (g or kg - must match units of $c$)
• $c$ = specific heat capacity
• $\Delta T$ = temperature change (°C or K)

What Specific Heat Means

Specific heat (c) is the energy needed to raise 1 gram of a substance by 1°C.

• High $c$ → temperature changes slowly (water)
• Low $c$ → temperature changes quickly (many metals)

Important insight students miss:
Two substances can absorb the same amount of heat and show different temperature changes if their specific heats differ.

If 100 g of aluminum and 100 g of water absorb 500 J:

• Aluminum’s temperature rises more
• Water’s rises less
  because water has a much higher $c$

Molar Heat Capacity

Same idea, but per mole instead of gram.
Sometimes problems give moles instead of mass.

3. Types of Calorimeters

Calorimeters measure heat indirectly through temperature change.

Coffee-Cup Calorimeter (Constant Pressure)

Coffee-cup calorimeter

• Insulated Styrofoam cup
• Measures temperature change of solution
• Pressure is constant (open to atmosphere)

At constant pressure:

$$q_{\text{reaction}} = \Delta H_{\text{reaction}}$$

This is the most common AP setup.

Bomb Calorimeter (Constant Volume)

Bomb calorimeter

• Sealed rigid container
• Often used for combustion reactions
• Measures temperature change of surrounding water

Because volume is constant, it measures internal energy, not directly ΔH (you don’t need deeper thermodynamics for AP).

4. Solving Calorimetry Problems

Basic Heating/Cooling

Example:
50.0 g of a metal warms from 22.0°C to 35.0°C.
Specific heat = 0.90 J/g°C.

1. $\Delta T = 35.0 - 22.0 = 13.0°C$
2. $q = (50.0)(0.90)(13.0)$
3. $q = 585$ J

Positive q → heat absorbed.

Watch your units. If mass is in kg but $c$ is J/g°C, convert first.

Two Substances Exchanging Heat

If no heat escapes:

$$m_{1} c_{1} \Delta T_{1} = - m_{2} c_{2} \Delta T_{2}$$

This is used to:

• Find unknown specific heat
• Find final temperature
• Show energy conservation

A larger temperature change does not mean more heat transferred. Mass and specific heat matter too. The AP loves giving data where one substance changes temperature a lot and the other only a little, and asking you to explain why energy is still conserved.

Dissolution in a Calorimeter

When a solid dissolves:

• Temperature increases → solution gained heat
  → reaction released heat
  → Exothermic (ΔH < 0)
• Temperature decreases → solution lost heat
  → reaction absorbed heat
  → Endothermic (ΔH > 0)

The dissolving process is the system.
The water/solution is the surroundings.

Students often flip the sign here. Always ask: Who changed temperature? That’s the surroundings.

5. Connecting q and ΔH

q is measured heat.
ΔH is enthalpy change.

In a constant-pressure calorimeter:

$$q_{\text{reaction}} = \Delta H_{\text{reaction}}$$

If the surroundings warm up, the reaction released heat. ΔH is negative.

If the surroundings cool down, the reaction absorbed heat. ΔH is positive.

Energy accounting always follows the First Law. Nothing disappears.