4.2 - Specific Heat Capacity

Heat Capacity

• Heat capacity, $C$: heat required to raise an object’s temperature by $1{}^{\circ }\mathrm{C}$.

• $Q$ is heat supplied in joules; $\Delta \theta$ is temperature change in ${}^{\circ }\mathrm{C}$. Unit of $C$: $\mathrm{J}{}^{\circ }{\mathrm{C}}^{-1}$.
• For the same heat supplied, an object with a higher heat capacity has a smaller temperature rise.
• Example: supplying 100 J raises X by $1{}^{\circ }\mathrm{C}$ and Y by $2{}^{\circ }\mathrm{C}$; $C_X=100\mathrm{J}{}^{\circ }{\mathrm{C}}^{-1}$ and $C_Y=50\mathrm{J}{}^{\circ }{\mathrm{C}}^{-1}$.
• For the same substance, greater mass gives greater heat capacity: a full kettle takes longer to boil than a half-filled kettle; a large bowl of soup remains hotter than a small bowl after cooling for the same period.
• Under sunlight for the same period, sand heats up faster than sea water because sand has a lower heat capacity.
• A car dashboard has a lower heat capacity than its fabric cushion and experiences a greater temperature rise under sunlight. Cement courts and grass also show different temperatures at noon.

Specific Heat Capacity

• Specific heat capacity, $c$: heat required to raise the temperature of 1 kg of a substance by $1{}^{\circ }\mathrm{C}$.

• $m$ is mass in kg; $\Delta \theta$ is temperature change in ${}^{\circ }\mathrm{C}$ or K. Units of $c$: $\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$ or $\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$.
• Heat capacity describes an object and depends on its mass; specific heat capacity compares substances on a 1 kg basis.
• Aluminium’s $c=900\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$: 1 kg needs 900 J for a $1{}^{\circ }\mathrm{C}$ rise.
• Water’s high $c$ allows it to absorb much heat with a small temperature rise, making it a good cooling agent.
• Metals generally have lower specific heat capacities than non-metals and heat up quickly when heat is supplied.

Substance	$c$ / $\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$
Water; sea water	4 200; 3 900
Ethanol; paraffin	2 500; 2 100
Cooking oil; olive oil	1 850; 1 890
Methane; steam at $100{}^{\circ }\mathrm{C}$	2 200; 2 020
Neon; air	1 030; 1 000
Aluminium; iron; copper	900; 450; 390
Gold; mercury; lead	300; 140; 130
Polycarbonate; wood	1 250; 1 700
Concrete; sand; glass	850; 800; 670

Experiment 4.1 - Specific Heat Capacity of Water

• Aim: determine the specific heat capacity of water.
• Apparatus: power supply, immersion heater, beaker, stopwatch, thermometer, retort stand and electronic balance. Materials: water and tissue paper.

1. Wrap the beaker in tissue paper. Place it on the balance and zero the reading.
2. Fill it three-quarters full with water and record water mass, $m$.
3. Immerse the heater and thermometer in the water, with the thermometer supported by the retort stand. Record initial temperature, ${\theta }_1$.
4. Switch on the heater and start timing together; observe the temperature reading.
5. After five minutes, switch off the heater. Record the highest reading as final temperature, ${\theta }_2$.

• Record heater power $P$ (W), heating time $t$ (s), mass $m$ (kg) and both temperatures.
• The immersion heater converts electrical energy into heat: $Q=Pt$; hence $Pt=mc({\theta }_2-{\theta }_1)$.

Experiment 4.2 - Specific Heat Capacity of Aluminium

• Aim: determine the specific heat capacity of aluminium.
• Apparatus: power supply, immersion heater, 1 kg aluminium block, stopwatch, thermometer and retort stand. Material: tissue paper.

1. Wrap the block in tissue paper and fit the heater and thermometer into the block’s holes.
2. Record initial block temperature, ${\theta }_1$.
3. Switch on the heater and start timing together.
4. After five minutes, switch off the heater and record the highest thermometer reading, ${\theta }_2$.

• Record $P$, $t$, $m$, ${\theta }_1$ and ${\theta }_2$; calculate $c=Pt/[m({\theta }_2-{\theta }_1)]$.

Applications and Natural Phenomena

Application	Explanation
Wooden houses	Wood heats slowly because of its high specific heat capacity; its insulating property also limits heat entering in hot climates or escaping in cold climates.
Woks and clay pots	Metal woks heat quickly for rapid frying. Clay pots have a high specific heat capacity and keep food hot longer.
Car radiator	A pump circulates water through the engine block to absorb heat, then to the radiator; fan-drawn cool air removes heat through cooling fins.
Space capsule	The outer layer needs a high specific heat capacity and melting point to withstand heating during atmospheric re-entry.
Green buildings	The Diamond Building uses a concrete roof insulated with styrofoam boards. Styrofoam has a high specific heat capacity, reducing heat absorption and indoor temperature.
Pot body and handle	Aluminium bodies heat quickly; plastic handles heat slowly and are safer to hold.

• Sea breeze, daytime: land has a lower specific heat capacity than the sea and heats faster. Warm air above land rises; cooler air moves from sea to land.
• Land breeze, night: the sea has a higher specific heat capacity than land and cools more slowly. Warm air above the sea rises; cooler air moves from land to sea.

Worked Calculations

• Heating a metal block: $m=0.5\mathrm{kg}$, $P=50\mathrm{W}$, $t=90\mathrm{s}$; temperature rises from 20 to $45{}^{\circ }\mathrm{C}$.

• Assumption: all heater energy enters the block; no heat is lost to the surroundings.
• Mixing water: 20 g at $100{}^{\circ }\mathrm{C}$ is mixed with 200 g at $28{}^{\circ }\mathrm{C}$. With final temperature $y$, equate heat released = heat absorbed:

• Assumption: heat passes only between the two water portions; none is exchanged with the surroundings.

Cluster Homes and Extreme Heat

• Cluster homes share three walls with neighbouring homes; doors and windows are at the front. This arrangement saves land, but residents can experience extreme heat during El Nino.