Transfer of Heat — Practice Quiz

A Physics cheat sheet for Transfer of Heat — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Conduction: Heat \(Q\) conducted in time \(t\) through a material of thermal conductivity \(k\), area \(A\), and length \(L\), with temperature difference \(\Delta T\).

$$Q = \frac{(kA \Delta T)t}{L}$$

Where: \(k\) = thermal conductivity

Stefan-Boltzmann Law (Radiation): Radiant energy \(Q\) emitted in time \(t\) by an object with emissivity \(e\), area \(A\), and temperature \(T\).

$$Q = e\sigma T^4 At$$

Where: \(\sigma\) = Stefan-Boltzmann constant \((5.67 \times 10^{-8} J/(s\cdot m^2\cdot K^4))\)

Net Radiant Power: Net power \(P_{net}\) emitted/absorbed by an object at temperature \(T\) in an environment at \(T_0\).

$$P_{net} = e\sigma A (T^4 - T_0^4)$$

Practice quiz

  1. A glass window has a thermal conductivity $k = 0.8 \text{ W}/(\text{m} \cdot \text{K})$, an area $A = 1.5 \text{ m}^2$, and a thickness $L = 0.005 \text{ m}$. If the temperature difference across the window is $\Delta T = 15 \text{ K}$, how much heat $Q$ is conducted through it in $t = 3600 \text{ s}$ (1 hour)?

    • $1.296 \times 10^8 \text{ J}$
    • $6.48 \times 10^7 \text{ J}$
    • $1.296 \times 10^6 \text{ J}$
    • $6.48 \times 10^5 \text{ J}$

    Answer: $1.296 \times 10^8 \text{ J}$

  2. According to the conduction formula $Q = \frac{(kA \Delta T)t}{L}$, if the length $L$ of a material through which heat is conducted is doubled, and all other parameters remain constant, how does the amount of heat $Q$ conducted change?

    • It doubles.
    • It is halved.
    • It quadruples.
    • It remains the same.

    Answer: It is halved.

  3. A perfectly black object ($e=1$) with a surface area $A = 0.2 \text{ m}^2$ is at a temperature of $T = 300 \text{ K}$. How much radiant energy $Q$ does it emit in $t = 60 \text{ s}$? Use the Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \text{ J}/(\text{s} \cdot \text{m}^2 \cdot \text{K}^4)$.

    • $551.1 \text{ J}$
    • $183.7 \text{ J}$
    • $1102.2 \text{ J}$
    • $275.5 \text{ J}$

    Answer: $551.1 \text{ J}$

  4. For an object emitting radiant energy according to the Stefan-Boltzmann Law ($Q = e\sigma T^4 At$), if its absolute temperature $T$ is doubled, by what factor does the emitted radiant energy $Q$ increase, assuming all other factors remain constant?

    • Factor of $2$
    • Factor of $4$
    • Factor of $8$
    • Factor of $16$

    Answer: Factor of $16$

  5. A surface with emissivity $e = 0.8$ and area $A = 0.5 \text{ m}^2$ is at a temperature $T = 350 \text{ K}$. The surrounding environment is at $T_0 = 290 \text{ K}$. Calculate the net radiant power $P_{net}$ for this surface. Use $\sigma = 5.67 \times 10^{-8} \text{ J}/(\text{s} \cdot \text{m}^2 \cdot \text{K}^4)$.

    • $105.2 \text{ W}$
    • $131.5 \text{ W}$
    • $84.2 \text{ W}$
    • $168.4 \text{ W}$

    Answer: $105.2 \text{ W}$

  6. Under what condition will the net radiant power $P_{net} = e\sigma A (T^4 - T_0^4)$ be zero?

    • When the object's temperature $T$ is much higher than the environment temperature $T_0$.
    • When the object's temperature $T$ is much lower than the environment temperature $T_0$.
    • When the object's temperature $T$ is equal to the environment temperature $T_0$.
    • When the emissivity $e$ is zero.

    Answer: When the object's temperature $T$ is equal to the environment temperature $T_0$.

  7. Two walls, Wall X and Wall Y, are made of the same material and have the same area and thickness. Wall X has a temperature difference of $10 \text{ K}$ across it, while Wall Y has a temperature difference of $20 \text{ K}$. How does the heat conducted through Wall Y compare to Wall X over the same time period?

    • Wall Y conducts half the heat of Wall X.
    • Wall Y conducts the same amount of heat as Wall X.
    • Wall Y conducts twice the heat of Wall X.
    • Wall Y conducts four times the heat of Wall X.

    Answer: Wall Y conducts twice the heat of Wall X.

  8. An object at $200 \text{ K}$ emits radiant energy at a rate of $P_1$. If its temperature is increased to $400 \text{ K}$, what is the new rate of radiant energy emission $P_2$, assuming all other factors (emissivity, area) remain constant?

    • $P_2 = 2 P_1$
    • $P_2 = 4 P_1$
    • $P_2 = 8 P_1$
    • $P_2 = 16 P_1$

    Answer: $P_2 = 16 P_1$

  9. A metal rod of length $L = 0.5 \text{ m}$ and cross-sectional area $A = 0.01 \text{ m}^2$ conducts $Q = 1000 \text{ J}$ of heat in $t = 10 \text{ s}$ when the temperature difference across its ends is $\Delta T = 5 \text{ K}$. What is the thermal conductivity $k$ of the metal?

    • $10 \text{ W}/(\text{m} \cdot \text{K})$
    • $50 \text{ W}/(\text{m} \cdot \text{K})$
    • $100 \text{ W}/(\text{m} \cdot \text{K})$
    • $200 \text{ W}/(\text{m} \cdot \text{K})$

    Answer: $100 \text{ W}/(\text{m} \cdot \text{K})$

  10. A sphere with emissivity $e = 0.9$ and surface area $A = 0.1 \text{ m}^2$ is in an environment at $T_0 = 293 \text{ K}$ ($20 \text{ \textdegree C}$). If the sphere is emitting net radiant power $P_{net} = 50 \text{ W}$, what is its approximate surface temperature $T$? Use $\sigma = 5.67 \times 10^{-8} \text{ J}/(\text{s} \cdot \text{m}^2 \cdot \text{K}^4)$.

    • $300 \text{ K}$
    • $320 \text{ K}$
    • $340 \text{ K}$
    • $360 \text{ K}$

    Answer: $340 \text{ K}$

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