Specific Heat and Thermal Conductivity - AP Physics 2

1. What does the negative sign in $q = -kA\frac{\Delta T}{\Delta x}$ indicate?

   Heat flows from high to low temperature. Heat flows down temperature gradient naturally.

2. What is the specific heat of water?

   $4.18 \text{ J/g°C}$. High value gives water thermal stability.

3. Find the specific heat capacity if $q=500 \text{ J}$, $m=2 \text{ kg}$, $\Delta T=5^{\circ}C$.

   $50 \text{ J/kg·K}$. $c = q/(m\Delta T) = 500/(2 \times 5) = 50$

4. What is the thermal conductivity of copper?

   Approximately $385 \text{ W/m·K}$. High thermal conductivity metal.

5. State Fourier's Law of Heat Conduction.

   Heat transfer rate $q = -kA\frac{\Delta T}{\Delta x}$. Fundamental equation for conductive heat transfer.

6. Which material typically has higher thermal conductivity: metal or wood?

   Metal. Metals conduct heat much better than wood.

7. Find $c$ if $q=750 \text{ J}$, $m=3 \text{ kg}$, $\Delta T=10^{\circ}C$.

   $25 \text{ J/kg·K}$. $c = q/(m\Delta T) = 750/(3 \times 10) = 25$

8. What is the specific heat if $q=200 \text{ J}$, $m=4 \text{ kg}$, $\Delta T=2^{\circ}C$?

   $25 \text{ J/kg·K}$. $c = q/(m\Delta T) = 200/(4 \times 2) = 25$

9. State the formula for thermal conductivity.

   $q = -kA\frac{\Delta T}{\Delta x}$. Fourier's Law relates heat flow to material properties.

10. Define specific heat capacity.

    Amount of heat required to raise 1 kg of substance by $1^{\circ}C$. Intensive property measuring thermal inertia.

11. What is the thermal conductivity of air?

    Approximately $0.024 \text{ W/m·K}$. Air is good thermal insulator.

12. What is the formula for specific heat capacity?

    $c = \frac{q}{m\Delta T}$. Rearranged from $q = mc\Delta T$.

13. What is the temperature change if $1000 \text{ J}$ is added to $2 \text{ kg}$ of aluminum ($c=900 \text{ J/kg·K}$)?

    $0.56^{\circ}C$. $\Delta T = q/(mc) = 1000/(2 \times 900) = 0.56$

14. Find $c$ if $q=750 \text{ J}$, $m=3 \text{ kg}$, $\Delta T=10^{\circ}\text{C}$.

    $25 \text{ J/kg·K}$. $c = q/(m\Delta T) = 750/(3 \times 10) = 25$

15. Calculate $\Delta T$ if $q=500 \text{ J}$, $m=1 \text{ kg}$, $c=250 \text{ J/kg·K}$.

    $2^{\circ}C$. $\Delta T = q/(mc) = 500/(1 \times 250) = 2$

16. What is the unit of specific heat capacity in SI?

    Joules per kilogram per Kelvin (J/kg·K). Energy per mass per temperature change.

17. What does $k$ represent in the thermal conductivity formula?

    Thermal conductivity. Material's intrinsic heat conduction property.

18. Find $\Delta T$ if $q=2500 \text{ J}$, $m=5 \text{ kg}$, $c=500 \text{ J/kg·K}$.

    $1^{\circ}C$. $\Delta T = q/(mc) = 2500/(5 \times 500) = 1$

19. What is the effect of high specific heat on temperature change?

    Smaller temperature change for given heat input. More energy needed for same temperature rise.

20. What is the role of area $A$ in the thermal conductivity equation?

    Cross-sectional area through which heat flows. Larger area increases heat transfer proportionally.

21. What does $q$ represent in heat equations?

    Heat transfer. Heat energy or heat flow rate.

22. Find the specific heat if $q=360 \text{ J}$, $m=2 \text{ kg}$, $\Delta T=2^{\circ}C$.

    $90 \text{ J/kg·K}$. $c = q/(m\Delta T) = 360/(2 \times 2) = 90$

23. Find the mass if $q=1500 \text{ J}$, $c=200 \text{ J/kg·K}$, $\Delta T=3^{\circ}C$.

    $2.5 \text{ kg}$. $m = q/(c\Delta T) = 1500/(200 \times 3) = 2.5$

24. Identify the meaning of $\Delta x$ in thermal conductivity.

    Thickness of the material. Greater thickness reduces heat transfer rate.

25. What is thermal conductivity?

    Measure of a material's ability to conduct heat. Material property for heat conduction efficiency.

26. What does $\Delta T$ represent in heat transfer formulas?

    Change in temperature. Final minus initial temperature.

27. What is the unit of thermal conductivity in SI?

    Watts per meter per Kelvin (W/m·K). Power per length per temperature difference.

28. Identify the symbol for specific heat capacity.

    $c$. Lowercase c is standard notation.

29. State the formula for calculating heat transfer.

    $q = mc\Delta T$. Relates heat to mass, specific heat, and temperature change.

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