Specific heat capacity, specific latent heat and heating curves

Specific heat capacity (SHC)

Specific heat capacity (c) is the energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K).

Units: J/(kg·°C) or J/(kg·K).

Equation: $$\Delta E = mc\Delta\theta$$

Where:

• ΔE = energy transferred (J)
• m = mass (kg)
• c = specific heat capacity (J/kg/°C)
• Δθ = temperature change (°C)

Example: Calculate the energy to heat 2 kg of water from 20°C to 80°C. (c_water = 4200 J/kg/°C) ΔE = 2 × 4200 × (80 − 20) = 2 × 4200 × 60 = 504,000 J = 504 kJ.

Why water is useful for heating systems: water has a very high SHC (4200 J/kg/°C) compared to most materials. It can absorb or release a lot of energy with a small temperature change.

Core Practical — measuring SHC of a solid

Core Practical 16: Determine the specific heat capacity of a solid metal block.

Equipment: metal block with two holes, electric immersion heater, thermometer, insulating jacket, joulemeter (or ammeter + voltmeter + stopwatch), balance.

Method:

1. Measure the mass of the block (m).
2. Insert heater and thermometer into the block; wrap in insulation.
3. Record starting temperature (θ₁).
4. Switch on heater; record energy supplied E (from joulemeter) and temperature at regular intervals.
5. When a significant temperature rise is achieved, switch off and record final temperature (θ₂).
6. Calculate: c = ΔE / (m × Δθ).

Sources of error:

• Heat loss to surroundings (reduces measured c → result too high if underestimated, or: energy actually transferred to block is less than measured → c appears larger than true value).
• Thermometer not in good thermal contact with block.
• Insulation not perfect.

Specific latent heat (SLH)

Specific latent heat (L) is the energy required to change the state of 1 kg of a substance WITHOUT changing its temperature.

Units: J/kg.

Equation: $$\Delta E = mL$$

Where:

• ΔE = energy transferred (J)
• m = mass (kg)
• L = specific latent heat (J/kg)

Two types:

• Specific latent heat of fusion (L_f): solid → liquid (or liquid → solid). Water: 334,000 J/kg.
• Specific latent heat of vaporisation (L_v): liquid → gas (or gas → liquid). Water: 2,260,000 J/kg.

Example: Energy to melt 0.5 kg of ice at 0°C: ΔE = mL = 0.5 × 334,000 = 167,000 J.

Heating and cooling curves

A heating curve shows temperature vs time as a substance is heated at a constant rate:

Temp
 |               ___________
 |              /
 |    _________/
 |   /
 |__/
 +-------------------------> Time

• Sloping sections: temperature rising → energy going into KE of particles (SHC applies).
• Flat sections (plateaus): state change occurring → temperature constant → energy going into breaking/forming intermolecular bonds (SLH applies). First plateau = melting; second = boiling.

During a state change, energy input goes into increasing potential energy of particles (breaking bonds), NOT kinetic energy. That's why temperature stays constant.