AP Physics 2: Algebra-Based Practice Quiz: Specific Heat and Thermal Conductivity

Correct Answer: A

Based on the equation Q = mcΔT, the energy required (Q) is directly proportional to the specific heat (c). Therefore, a material with a higher specific heat requires more energy to achieve the same temperature change (ΔT) for a given mass (m).

Correct Answer: B

From the equation Q=mcΔT, we can rearrange to ΔT = Q/(mc). Since the energy added (Q) and the specific heat (c) are the same for both blocks, the temperature change (ΔT) is inversely proportional to the mass (m). Because Block X has twice the mass, it will experience half the temperature change of Block Y. Therefore, Block Y has twice the ΔT of Block X.

Correct Answer: C

The equation for the rate of energy transfer by conduction is (Q/Δt) = (kAΔT)/L. The rate of energy transfer (Q/Δt) is directly proportional to the thermal conductivity (k). Therefore, a good thermal conductor has a high value of k, which results in a high rate of energy transfer.

Correct Answer: D

The rate of heat transfer is given by (Q/Δt) = (kAΔT)/L. The rate is inversely proportional to the thickness (L). If the thickness L is doubled to 2L, the rate of heat transfer will be divided by 2, meaning it will be halved.

Correct Answer: B

According to the equation Q=mcΔT, which can be rearranged to ΔT = Q/(mc), the temperature change (ΔT) is inversely proportional to the specific heat (c) when energy (Q) and mass (m) are constant. Since substance B has a lower specific heat, it will experience a larger temperature change.

Correct Answer: D

The rate of heat transfer is P = (Q/Δt) = (kAΔT)/L. The new rate, P', will be P' = (k(2A)ΔT)/(L/2). This simplifies to P' = 4 * (kAΔT)/L. Since the original rate P = (kAΔT)/L, the new rate is 4P.

Correct Answer: D

The content explicitly states, 'The thermal conductivity of a material is an intrinsic property of that material that depends on the arrangement and interactions of the atoms that make up the material.' The other options are extrinsic properties (A, C) or external conditions (B).

Correct Answer: B

Using the equation Q=mcΔT, we can solve for ΔT: ΔT = Q / (mc). Plugging in the values: ΔT = 4000 J / (2 kg * 500 J/(kg·K)) = 4000 / 1000 = 4 K.

Correct Answer: B

To keep a beverage cold, the goal is to minimize the rate of heat transfer from the warmer surroundings into the container. According to (Q/Δt) = (kAΔT)/L, a low thermal conductivity (k) is required to reduce this rate. A high specific heat (c) is also beneficial, as it means the insulating material itself can absorb some heat from the outside without its own temperature increasing significantly, thus maintaining a lower temperature on the interior surface.

Correct Answer: C

The specific heat (c) is an intrinsic property of a material, meaning it is a characteristic of the substance itself, regardless of the amount or shape. Mass (m) is an extrinsic property, while Q and ΔT are measures of energy transfer and its effect.

Correct Answer: C

The speed at which heat travels up the spoon handle is determined by the rate of energy transfer by conduction, (Q/Δt). The equation (Q/Δt) = (kAΔT)/L shows that this rate is directly proportional to the thermal conductivity (k). A material that transfers heat quickly, like metal, has a high k value compared to an insulator like wood.

Correct Answer: B

The relationship is given by ΔT = Q/(mc). The original temperature change is ΔT_original = Q/(mc). For the new scenario, the temperature change is ΔT_new = (2Q) / ((4m)c). Factoring out the numbers gives ΔT_new = (2/4) * (Q/(mc)) = (1/2) * ΔT_original. The new temperature change will be half of the original.

Correct Answer: D

The rate of heat transfer is (Q/Δt) = (kAΔT)/L. We can rearrange to solve for the time interval: Δt = QL/(kAΔT). For the original bar, Δt_orig = QL/(kAΔT). For the new bar, the time will be Δt_new = Q(2L)/(k(A/2)ΔT). Simplifying the coefficients gives Δt_new = (2/(1/2)) * (QL/(kAΔT)) = 4 * (QL/(kAΔT)). Therefore, Δt_new = 4Δt_orig.

Correct Answer: B

The question asks for the total amount of energy (Q) required to change the temperature (ΔT) of an object with a specific mass (m). The equation Q=mcΔT directly relates these quantities. The other equation, (Q/Δt) = (kAΔT)/L, describes the rate of energy transfer by conduction, not the total energy required for a temperature change.