Lesson summary
14.3.1 Specific Heat Capacity — AS PHYSICS 9702 notes: Define specific heat capacity, use Q = mcΔθ and describe how c is measured.Specific heat capacity c — the energy required per unit mass to raise the temperature of a substance by one kelvin, without a change of stateEquation …
- Typical values
- What the symbols mean
- Heat capacity of an object
- Electrical heating
- Heating graph
- Heating and cooling systems
Section 1 of 10Definition
Specific heat capacity c
- Specific heat capacity c the energy required per unit mass to raise the temperature of a substance by one kelvin, without a change of state
Equation
- Equation c = Q/(mΔθ)
- Q is the thermal energy in J
- m is the mass in kg
- Δθ is the temperature change in K or °C, which has the same size on both scales
- c is in J kg⁻¹ K⁻¹
Typical values
- Typical values water 4200, ice 2100, aluminium 900, copper 390 and lead 130 J kg⁻¹ K⁻¹
- The value for water is unusually high
Meaning
- Meaning a low c heats up and cools down quickly, a high c heats up and cools down slowly
Section 2 of 10The equation in use
1Q
Q mcΔθ
- positive Δθ means energy absorbed and negative Δθ means energy releasedWhat the symbols mean: E, Q or q = energy transferred (J) · m = mass · c = specific heat capacity (J kg−1 °C−1; water 4.18 J g−1 °C−1) · ΔT or Δθ = temperature change (°C or K)
- (kg; g in chemistry calorimetry)
2Heat capacity of an object
- C = Q/Δθ = mc in J K⁻¹
- For a mixture of objects, add the energy changes
3Electrical heating
- Electrical heating with all the energy used, Pt = mcΔθ, so ΔT/Δt = P/(mc)
4Heating graph
- Heating graph temperature against time is a straight line with gradient P/(mc)
- A steep graph means a small heat capacity
Section 3 of 10Why water is special
Why water is special
Climate
- Climate large bodies of water warm and cool slowly, so coastal climates are milder than inland ones
Heating and cooling systems
- Heating and cooling systems central heating and car cooling use water because each kilogram carries a lot of energy for a modest temperature change
The body
- The body mostly water, so it resists rapid temperature changes
Metals
- Metals copper with small c warms quickly, whereas water in the same pan takes much longer
Section 4 of 10Measuring c electrically
Measuring c electrically
Place an electric heater and thermometer in holes in the metal block
- Place an electric heater and thermometer in holes in the metal block add a drop of oil for good thermal contact
Lag the block with insulation
Record the starting temperature, then switch on the heater and measure the current I and p.d. V
After a time t record the final temperature
- After a time t record the final temperature the energy supplied is Q = IVt
Calculate
- Calculate c = IVt/(mΔθ)
Graph method
- Graph method plot temperature against time and use the gradient to average out random error
Liquids
- Liquids immerse the heater in a lagged calorimeter and stir to keep the temperature uniform
Section 5 of 10Errors in the electrical method
1Energy lost to the surroundings
- Energy lost to the surroundings more energy appears to be needed, so the measured c is too high
2Delay in spreading
- Delay in spreading energy takes time to spread through the block
3Heat capacity of the heater and thermometer
- Heat capacity of the heater and thermometer they absorb some of the energy
4Reducing the net effect of losses
- Reducing the net effect of losses use lagging and a lid, and start slightly below room temperature and finish slightly above
Section 6 of 10Method of mixtures
Principle
- Principle when a hot sample is dropped into cooler water in an insulated container, energy lost by the sample equals energy gained by the water and container at equilibrium
Calculation
- Calculation use c for water 4200 J kg⁻¹ K⁻¹ to find c of the metal
- Equate magnitudes, since Δθ for the hot object is negative
Requirements
- Requirements careful insulation, a quick transfer and stirring
Section 7 of 10Links and cautions
Microscopic view
- Microscopic view the energy supplied raises the vibrational kinetic and potential energy of the atoms of a solid
- For a monatomic ideal gas at constant volume the energy is (3/2)nRΔT
Calorimetry
- Calorimetry include the container, stirrer and thermometer through their heat capacities
Change of state
- Q = mcΔθ holds only while no change of state occurs
Section 8 of 10More from the specification
1
Thermal energy absorption in crystalline solids
- Thermal energy absorption in crystalline solids supplying known heat energy in joules raises the temperature of solid metals according to their specific heat capacity.
2
Specific Heat Capacity Equation
- The specific heat capacity c of a material is the amount of thermal energy required to raise the temperature of 1 kg of the substance by 1 °C (or 1 K) without a change of state: ΔE = m c ΔT.
3
Specific Latent Heat of Fusion vs. Vaporisation
- Specific latent heat is the thermal energy per unit mass required to change state at constant temperature;
- latent heat of fusion (Lf) occurs during melting/freezing,
- while latent heat of vaporisation (Lv) occurs during boiling/condensing to completely break intermolecular bonds between molecules.
4
Electrical Power and Energy Heating Calculations
- When heating water in an electric kettle of electrical power P, total energy supplied over time t is calculated via E = P t; equating this to m c ΔT allows calculation of heating efficiency and thermal losses.
- (plus m Lv if boiled)
5
Microscopic Behavior During Phase Changes
- During melting and boiling, temperature remains constant because added thermal energy increases potential energy rather than kinetic energy, overcoming intermolecular attractive forces between molecules.
6
Latent heat of vaporisation
- Latent heat of vaporisation thermal energy required to convert unit mass of liquid into gas during boiling without changing temperature.
7
Latent heat of fusion
- Latent heat of fusion energy needed to melt unit mass of solid into liquid at constant melting temperature.
8
Electrical kettle power
- Electrical kettle power multiplying electrical heating power by elapsed time gives the total thermal energy transferred to the liquid.
9
Fusion
- Joining of light nuclei into a heavier one.
10
Boiling
- Liquid becoming gas throughout the liquid at the boiling point
11
Melting
- Change from solid to liquid.
12
Molecule
- Tiny particle of the fluid, too small to be seen.
13
Joule
- Unit of energy, 1 kg·m2/s2.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Specific heat capacity | energy required per unit mass to raise the temperature by one kelvin |
| Heat capacity | energy required to raise the temperature of an object by one kelvin, C = mc |
| Calorimeter | an insulated container used to measure energy transfers |
| Method of mixtures | finding c by equating energy lost by a hot sample to energy gained by cooler water |
| Lagging | insulation used to reduce energy loss |
| Thermal contact | close contact that allows efficient energy transfer |
Section 10 of 10Exam technique
1
Using different temperature units for Δθ — the change has the same size in °C and K.
2
Forgetting to convert grams to kilograms — use m in kg.
3
Ignoring the container in calorimetry — include its heat capacity when given.
4
Using Q = mcΔθ during melting or boiling — the temperature is constant, so use Q = mL.