Heat & Thermo flash cards

1. 1.Distinguish heat from temperature.

   Temperature is a measure of the average kinetic energy of molecules (an intensive property, unit K). Heat is energy in transit due to a temperature difference (an extensive quantity of energy, unit J). Heat flows spontaneously from higher to lower temperature.

   Hint: One is a state property, the other is energy on the move.

2. 2.State the relations between the Celsius, Kelvin and Fahrenheit scales.

   $T_K = T_C + 273.15$ and $\frac{T_C}{5} = \frac{T_F - 32}{9}$. A change of $1\,^\circ$C equals a change of $1$ K, and equals a change of $1.8\,^\circ$F.

   Hint: Kelvin offset 273.15; C:F ratio 5:9 for intervals.

3. 3.Write the formula for linear thermal expansion and define $\alpha$.

   $L = L_0(1 + \alpha\,\Delta T)$, so $\Delta L = L_0\alpha\,\Delta T$. Here $\alpha$ is the coefficient of linear expansion (unit $\mathrm{K}^{-1}$), the fractional change in length per unit temperature rise.

   Hint: $\Delta L / L_0 = \alpha\,\Delta T$.

4. 4.How are the coefficients of area ($\beta$) and volume ($\gamma$) expansion related to the linear coefficient $\alpha$ for an isotropic solid?

   $\beta = 2\alpha$ and $\gamma = 3\alpha$, so $\alpha : \beta : \gamma = 1 : 2 : 3$. These follow from $(1+\alpha\Delta T)^2$ and $(1+\alpha\Delta T)^3$ keeping only first-order terms.

   Hint: Ratio 1:2:3 for isotropic solids.

5. 5.A metal plate with a hole is heated. Does the hole get bigger or smaller?

   The hole gets bigger. Every linear dimension scales by $(1+\alpha\Delta T)$, including the hole, exactly as if the removed disc material were still present. The hole expands like the surrounding metal.

   Hint: Cavities expand like solid material of the same shape.

6. 6.What is thermal stress in a rod clamped rigidly at both ends and heated by $\Delta T$?

   The rod cannot expand, so a compressive stress develops: $\text{stress} = Y\alpha\,\Delta T$, and the compressive force $F = YA\alpha\,\Delta T$, where $Y$ is Young's modulus and $A$ the cross-section. It is independent of length.

   Hint: Prevented strain $\alpha\Delta T$ times $Y$; length cancels.

7. 7.Explain the anomalous expansion of water and its significance.

   Between $0\,^\circ$C and $4\,^\circ$C water contracts on heating; density is maximum at $4\,^\circ$C. Below $4\,^\circ$C it expands on cooling. So ice and the coldest water float, letting lakes freeze top-down and aquatic life survive beneath.

   Hint: Maximum density at 4 °C.

8. 8.Why does a bimetallic strip bend on heating, and what is it used for?

   Two bonded metals have different $\alpha$; on heating the metal with larger $\alpha$ expands more, forcing the strip to curve toward the lower-$\alpha$ side. Used in thermostats and thermal switches to open/close circuits.

   Hint: Different expansion of the two layers → curvature.

9. 9.Why does a pendulum clock run slow in summer, and by how much per unit temperature?

   Rod length increases, so period $T = 2\pi\sqrt{L/g}$ increases and the clock loses time. Fractional time lost per second $= \tfrac{1}{2}\alpha\,\Delta T$; loss per day $\approx \tfrac{1}{2}\alpha\,\Delta T \times 86400$ s.

   Hint: $\Delta T/T = \tfrac12\,\alpha\,\Delta\theta$.

10. 10.How does the apparent expansion of a liquid relate to its real (absolute) expansion?

    $\gamma_{\text{apparent}} = \gamma_{\text{real}} - \gamma_{\text{vessel}}$, where $\gamma_{\text{vessel}} = 3\alpha_{\text{glass}}$. The liquid rises relative to the container only by the excess of its real expansion over the container's volume expansion.

    Hint: Subtract the container's volume expansion.

11. 11.Define specific heat capacity and write the heat equation.

    Specific heat $c$ is the heat needed to raise unit mass by $1$ K: $Q = mc\,\Delta T$ (unit $\mathrm{J\,kg^{-1}K^{-1}}$). Molar heat capacity $C = Mc$ uses moles instead: $Q = nC\,\Delta T$.

    Hint: $Q = mc\,\Delta T$.

12. 12.State the principle of calorimetry.

    In an isolated system, heat lost by hot bodies equals heat gained by cold bodies: $\sum Q_{\text{lost}} = \sum Q_{\text{gained}}$. It expresses conservation of energy with no heat exchanged with the surroundings.

    Hint: Heat lost = heat gained.

13. 13.Define latent heat and give the two types.

    Latent heat $L$ is the heat per unit mass absorbed or released during a phase change at constant temperature: $Q = mL$. Latent heat of fusion (solid↔liquid) and latent heat of vaporization (liquid↔gas).

    Hint: Phase change at constant T; $Q=mL$.

14. 14.Why does temperature stay constant during a phase change even though heat is supplied?

    The supplied heat breaks intermolecular bonds and increases potential energy, not kinetic energy. Since temperature reflects average kinetic energy, it remains constant until the phase change is complete.

    Hint: Energy goes into potential energy / bonds, not KE.

15. 15.Define the water equivalent of a calorimeter.

    Water equivalent $W$ is the mass of water that would absorb the same heat as the body for the same temperature rise: $W = \frac{mc}{c_{\text{water}}}$. It lets a container's heat capacity be added as an equivalent mass of water.

    Hint: Mass of water with the same heat capacity.

16. 16.What is a heating curve (temperature vs heat supplied for ice → steam)?

    Sloped segments (single phase, $T$ rises, slope $=1/mc$) alternate with flat plateaus (phase change at $0\,^\circ$C and $100\,^\circ$C, $T$ constant while $Q=mL$). Flatter slope means larger specific heat.

    Hint: Slopes = heating a phase; plateaus = phase changes.

17. 17.List the three modes of heat transfer and the medium each needs.

    Conduction: through matter without bulk motion (needs a medium, mainly solids). Convection: bulk motion of fluid (needs a fluid). Radiation: electromagnetic waves (needs no medium, works in vacuum).

    Hint: Contact, fluid flow, EM waves.

18. 18.State the law of steady-state conduction (Fourier's law).

    $\frac{dQ}{dt} = -kA\frac{dT}{dx}$; for a slab of thickness $L$ with faces at $T_1 > T_2$: $\frac{dQ}{dt} = \frac{kA(T_1-T_2)}{L}$. Here $k$ is thermal conductivity ($\mathrm{W\,m^{-1}K^{-1}}$).

    Hint: Rate ∝ area × temperature gradient.

19. 19.Define thermal resistance and its analogy to electrical resistance.

    $R_{\text{th}} = \frac{L}{kA}$, so the heat current $\frac{dQ}{dt} = \frac{\Delta T}{R_{\text{th}}}$. Temperature difference plays the role of voltage and heat current that of electric current (Ohm's-law analogy).

    Hint: $R = L/kA$; $\Delta T$ ↔ V, heat rate ↔ I.

20. 20.How do you combine thermal resistances in series and in parallel?

    Series (slabs stacked along heat flow): $R = R_1 + R_2 + \dots$ (same heat current). Parallel (side by side, same $\Delta T$): $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$

    Hint: Exactly like electrical resistors.

21. 21.In the steady state, what is the junction temperature of two rods of conductivities $k_1,k_2$ (equal length and area) joined in series with ends at $T_1$ and $T_2$?

    Equal heat currents give $T = \dfrac{k_1 T_1 + k_2 T_2}{k_1 + k_2}$. It is the conductivity-weighted mean of the two end temperatures.

    Hint: Weight each end temperature by that rod's conductivity.

22. 22.What is convection, and what distinguishes natural from forced convection?

    Convection transfers heat by bulk movement of a heated fluid. Natural convection is driven by buoyancy from density differences of the heated fluid; forced convection uses an external agent (fan, pump) to move the fluid.

    Hint: Buoyancy-driven vs externally driven fluid flow.

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