Thermal Energy Transfer

Internal energy, the first law of thermodynamics, specific heat capacity, specific latent heat, and continuous flow calorimetry.

Spec Points Covered
  • Define internal energyThe capacity to do work. Measured in joules (J).The sum of the randomly distributed kinetic and potential energies of all the molecules in a system. as the sum of randomly distributed kinetic and potential energies.
  • State the first law of thermodynamics qualitatively.
  • Define specific heat capacityThe energyThe capacity to do work. Measured in joules (J). required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C). and apply $Q = mc \Delta$ theta.
  • Define specific latent heatThe energyThe capacity to do work. Measured in joules (J). required to change the state of 1 kg of a substance without changing its temperature. of fusion and vaporisation and apply $Q = mL$.
  • Describe the continuous flow calorimetry method and derive c from two flow rates.
Notes
01 Internal energy is the total random kinetic and potential energy of all particles Internal energy 3.6.2.1 → 02 The first law of thermodynamics is conservation of energy applied to thermal systems First law of thermodynamics 3.6.2.1 → 03 Specific heat capacity: the energy to raise 1 kg by 1 degree Specific heat capacity 3.6.2.1 → 04 Continuous flow calorimetry eliminates heat losses $c = \frac{Q_2 - Q_1}{(m_2 - m_1)\Delta\theta}$ 3.6.2.1 → 05 Specific latent heat: energy to change state without changing temperature Specific latent heat 3.6.2.1 → 06 During a phase change, potential energy changes but kinetic energy does not 3.6.2.1 → 07 Thermal equilibrium problems combine Q = mc delta theta and Q = mL $Q_{\text{heat solid}} + Q_{\text{melt}} + Q_{\text{heat liquid}} = -Q_{\text{warm substance}}$ 3.6.2.1 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Thermal energy change
$$\Delta Q = mc\Delta\theta$$
  • Where:
    • $\Delta Q$ = change in thermal energy (J)
    • $m$ = mass (kg)
    • $c$ = specific heat capacity (J kg^{-1} \(K^{-1}\))
    • $\Delta \theta$ = change in temperature (K or degrees C)
Delta theta is the same in kelvin and Celsius. No conversion needed.
Continuous flow calorimetry
$$c = \frac{Q_2 - Q_1}{(m_2 - m_1)\Delta\theta}$$
  • Where:
    • $c$ = specific heat capacity (J kg^{-1} \(K^{-1}\))
    • $Q_1$ = electrical energy in run 1 = I_1 V_1 t_1 (J)
    • $Q_2$ = electrical energy in run 2 = I_2 V_2 t_2 (J)
    • $m_1$ = mass of fluid in run 1 (kg)
    • $m_2$ = mass of fluid in run 2 (kg)
    • $\Delta\theta$ = temperature rise (same in both runs) (K)
Derived by subtracting two runs of IVt = mc delta theta + E_lost. E_lost cancels.
Energy for change of state
$$Q = mL$$
  • Where:
    • $Q$ = thermal energy for change of state (J)
    • $m$ = mass (kg)
    • $L$ = specific latent heat (J kg^{-1})
L is either L_fusion (solid to liquid) or L_vaporisation (liquid to gas). Temperature does not change.
Electrical energy input
$$Q = IVt$$
  • Where:
    • $Q$ = electrical energy (J)
    • $I$ = current (A)
    • $V$ = potential difference (V)
    • $t$ = time (s)
Used in continuous flow and other heating experiments. Equivalent to Q = Pt.
Q Retrieval Practice All 14 Questions →
Q1. Define internal energyThe sum of the randomly distributed kinetic and potential energies of all the molecules in a system..
The sum of the randomly distributed kinetic and potential energies of all the particles in a body.
Q2. State two ways to increase the internal energyThe sum of the randomly distributed kinetic and potential energies of all the molecules in a system. of a system.
  • Do work on the system (e.g. compress a gas).
  • Transfer thermal energy to the system (heat it).
Q3. State the first law of thermodynamics.
The internal energy of a system is increased when energy is transferred to it by heating or when work is done on it.
Q4. Define specific heat capacityThe energy required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C)..
The amount of thermal energy required to raise the temperature of 1 kg of a substance by 1 K (or 1 degree C) without a change of state.
Q5. Write the equation for thermal energy change.
delta Q = mc delta theta, where m = mass, c = specific heat capacityThe energy required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C)., delta theta = temperature change.