Heat & Thermo flash cards

1. 1.Define coefficient of linear expansion $\alpha$ and give its SI unit.

   $\alpha = \dfrac{\Delta L}{L\,\Delta T}$ — fractional increase in length per unit rise in temperature. SI unit: $\text{K}^{-1}$ (or $^\circ\text{C}^{-1}$).

   Hint: Fractional change in length per degree.

2. 2.How are coefficients of linear ($\alpha$), superficial ($\beta$) and cubical ($\gamma$) expansion related for an isotropic solid?

   $\alpha : \beta : \gamma = 1 : 2 : 3$, i.e. $\beta = 2\alpha$ and $\gamma = 3\alpha$.

   Hint: Area involves two dimensions, volume three.

3. 3.A metal rod of length $L$ expands by $\Delta L$ on heating through $\Delta T$. Write the expression for its new length.

   $L' = L(1 + \alpha\,\Delta T)$, where $\alpha$ is the coefficient of linear expansion.

   Hint: Linear expansion formula.

4. 4.Why does water show anomalous expansion, and what is special about $4^\circ\text{C}$?

   Between $0^\circ\text{C}$ and $4^\circ\text{C}$ water contracts on heating; below $4^\circ$ it expands on cooling. Water has maximum density (minimum volume) at $4^\circ\text{C}$.

   Hint: Density is maximum, not minimum.

5. 5.How does anomalous expansion of water help aquatic life in cold climates?

   Water at $4^\circ\text{C}$ (densest) sinks to the bottom while ice ($0^\circ\text{C}$, less dense) floats on top. The lake freezes top-down, so water below stays liquid and aquatic life survives.

   Hint: Ice floats; denser water sinks.

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

   Thermal stress $= Y\alpha\,\Delta T$, where $Y$ is Young's modulus. It is independent of the length and area of cross-section.

   Hint: Stress $= Y \times$ strain; strain $= \alpha\Delta T$.

7. 7.Define specific heat capacity and give its SI unit.

   Heat required to raise the temperature of unit mass of a substance by one degree: $c = \dfrac{Q}{m\,\Delta T}$. SI unit: $\text{J kg}^{-1}\text{K}^{-1}$.

   Hint: Per unit mass, per degree.

8. 8.What is molar specific heat capacity and its SI unit?

   Heat needed to raise one mole of a substance by one degree: $C = \dfrac{Q}{n\,\Delta T}$. SI unit: $\text{J mol}^{-1}\text{K}^{-1}$.

   Hint: Per mole instead of per kg.

9. 9.Why can a substance have two distinct molar specific heats, $C_p$ and $C_V$?

   Heat supplied depends on the process. At constant pressure the gas also does work in expanding, so $C_p > C_V$. At constant volume no external work is done.

   Hint: Constant pressure gas does work on surroundings.

10. 10.State the principle of calorimetry.

    When bodies at different temperatures are mixed (with no heat loss to surroundings), heat lost by hotter bodies = heat gained by colder bodies.

    Hint: Conservation of energy for heat exchange.

11. 11.Define latent heat of fusion and latent heat of vaporization.

    Latent heat is heat per unit mass absorbed/released during a phase change at constant temperature: $Q = mL$. Fusion = solid $\leftrightarrow$ liquid; vaporization = liquid $\leftrightarrow$ gas.

    Hint: Phase change at constant temperature.

12. 12.For water, give approximate values of latent heat of fusion and vaporization.

    Latent heat of fusion $L_f \approx 3.34\times10^5\,\text{J kg}^{-1}$ (80 cal/g); latent heat of vaporization $L_v \approx 22.6\times10^5\,\text{J kg}^{-1}$ (540 cal/g).

    Hint: 80 and 540 cal/g.

13. 13.Why does temperature stay constant during melting or boiling even though heat is being supplied?

    The absorbed heat (latent heat) is used to break intermolecular bonds / change the state, increasing potential energy of molecules, not their kinetic energy — so temperature (mean KE) is unchanged.

    Hint: Heat goes into potential energy, not KE.

14. 14.What is a triple point? What is the triple point of water?

    The unique temperature and pressure at which solid, liquid and vapour coexist in equilibrium. For water: $273.16\,\text{K}$ at $0.61\,\text{kPa}$.

    Hint: All three phases coexist; $273.16$ K.

15. 15.Name the three modes of heat transfer and state which needs no medium.

    Conduction, convection, and radiation. Radiation requires no material medium (it can travel through vacuum).

    Hint: Only one works through vacuum.

16. 16.State the equation for steady-state heat conduction through a slab (Fourier's law).

    $\dfrac{Q}{t} = \dfrac{kA\,(T_1 - T_2)}{L}$, where $k$ is thermal conductivity, $A$ area, $L$ thickness, $(T_1-T_2)$ temperature difference.

    Hint: Rate $\propto$ area and temperature gradient.

17. 17.Define thermal conductivity $k$ and give its SI unit.

    $k$ is the rate of heat flow per unit area per unit temperature gradient in the steady state. SI unit: $\text{W m}^{-1}\text{K}^{-1}$.

    Hint: Property of the material; units W/(m·K).

18. 18.What is thermal resistance of a slab and how does it combine in series?

    Thermal resistance $R = \dfrac{L}{kA}$. In series, resistances add: $R = R_1 + R_2 + \dots$ (analogous to electrical resistors).

    Hint: Like resistors in series; $R = L/kA$.

19. 19.Explain how convection differs from conduction.

    In conduction heat passes through a medium without bulk motion of the medium (energy passed particle to particle). In convection heat is carried by actual bulk movement of the heated fluid (currents).

    Hint: Bulk movement of fluid vs. particle-to-particle.

20. 20.Give two everyday examples of natural convection.

    Sea/land breezes, trade winds, boiling of water, room heating by radiators, and monsoon circulation are driven by convection currents.

    Hint: Breezes and boiling water.

21. 21.State Stefan-Boltzmann law for a black body.

    The power radiated per unit area of a black body is $E = \sigma T^4$, where $\sigma = 5.67\times10^{-8}\,\text{W m}^{-2}\text{K}^{-4}$ and $T$ is absolute temperature.

    Hint: Radiated power $\propto T^4$.

22. 22.How is the Stefan-Boltzmann law modified for a body of emissivity $e$ radiating to surroundings at $T_0$?

    Net power radiated: $P = e\sigma A (T^4 - T_0^4)$, where $e$ is the emissivity ($0 \le e \le 1$) and $A$ the surface area.

    Hint: Include emissivity and subtract surroundings' $T_0^4$.

23. 23.Define a perfect black body.

    A body that absorbs all radiation of every wavelength incident on it (absorptivity = 1) and is also the best possible emitter at a given temperature.

    Hint: Absorbs everything; perfect emitter.

24. 24.State Kirchhoff's law of thermal radiation.

    At a given temperature and wavelength, the ratio of emissive power to absorptive power is the same for all bodies and equals that of a black body. Good absorbers are good emitters.

    Hint: Good absorbers are good emitters.

25. 25.State Wien's displacement law.

    The wavelength of maximum spectral emission of a black body is inversely proportional to its absolute temperature: $\lambda_m T = b$, with $b = 2.9\times10^{-3}\,\text{m K}$.

    Hint: $\lambda_m \propto 1/T$.

26. 26.Using Wien's law, explain why a heated body changes colour from red to white as it gets hotter.

    As $T$ rises, $\lambda_m = b/T$ decreases, so the peak shifts from longer (red) to shorter (blue) wavelengths. A hotter body emits more across the spectrum, appearing white.

    Hint: Higher $T$ → shorter peak wavelength.

27. 27.State Newton's law of cooling.

    For a small temperature excess, the rate of loss of heat of a body is proportional to the temperature difference between the body and its surroundings: $-\dfrac{dT}{dt} \propto (T - T_0)$.

    Hint: Cooling rate $\propto$ temperature excess.

28. 28.Under what condition is Newton's law of cooling a good approximation of Stefan's law?

    When the temperature difference between the body and surroundings is small; then $T^4 - T_0^4 \approx 4T_0^3(T - T_0)$, giving a rate proportional to $(T - T_0)$.

    Hint: Small temperature difference.

29. 29.Define absolute (Kelvin) temperature and its relation to Celsius.

    Kelvin is the SI temperature scale with $0\,\text{K}$ as absolute zero. $T(\text{K}) = t(^\circ\text{C}) + 273.15$.

    Hint: Add 273.15 to Celsius.

30. 30.State Boyle's law.

    At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: $PV = \text{constant}$ (isothermal).

    Hint: $P \propto 1/V$ at constant $T$.

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