Specific Heat Capacity

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

$\boxed{\Delta E = m \times c \times \Delta\theta}$

Where:

• $\Delta E$ = energy transferred (J)
• $m$ = mass (kg)
• $c$ = specific heat capacity (J/kg°C)
• $\Delta\theta$ = change in temperature (°C)

Units of $c$: J/kg°C (or J/kg·K — the values are the same since a 1°C change equals a 1 K change).

Common Values

Water has an exceptionally high specific heat capacity — this is why:

• It takes a long time to boil water
• Oceans moderate coastal temperatures
• Water is used as a coolant in engines and power stations
• Central heating systems use water to carry thermal energy

$m = \frac{\Delta E}{c \times \Delta\theta} \qquad c = \frac{\Delta E}{m \times \Delta\theta} \qquad \Delta\theta = \frac{\Delta E}{m \times c}$

Aim

To measure the specific heat capacity of a solid (e.g., aluminium block) or liquid (e.g., water).

Equipment

• Insulated metal block (with holes for heater and thermometer) or beaker of water
• Electric immersion heater
• Thermometer (or temperature sensor)
• Joulemeter (or ammeter + voltmeter + stopwatch)
• Balance
• Insulation (lagging)

Method (Metal Block)

1. Measure the mass of the metal block
2. Insert the heater and thermometer into the block
3. Record the initial temperature
4. Switch on the heater and record energy supplied (using joulemeter) and temperature at regular intervals
5. After heating for a suitable time, switch off and record the highest temperature
6. Calculate $c$ using the equation

Method (Water)

1. Measure the mass of water in an insulated beaker
2. Record initial temperature
3. Heat with immersion heater, recording energy and temperature
4. Calculate $c$

Calculating Energy Without a Joulemeter

$E = P \times t = I \times V \times t$

Where $P$ = power, $I$ = current, $V$ = voltage, $t$ = time.

Sources of Error

• Energy loss to surroundings → measured $c$ will be too high (more energy needed than expected)
• Insulation reduces this error
• Thermometer position — may not measure the hottest/average temperature
• Thermal lag — temperature continues rising after heater is switched off

• Specific heat capacity = energy to raise 1 kg by 1°C
• $\Delta E = mc\Delta\theta$
• Water has a very high SHC (4200 J/kg°C)
• Required practical: heat a block/water, measure energy and temperature change
• Key error: energy loss to surroundings (use insulation)