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Copper Rod Heat Absorption and Temperature Change

Created by @nathanedwards
 at November 1st 2023, 11:09:07 pm.
AP_Physics_2-Questions
#heat-transfer
#ap-physics-2
#copper-rod

AP Physics 2 Exam Question:

A copper rod measures 1.5 meters in length and has a cross-sectional area of 0.008 square meters. The rod is initially at a temperature of 20°C.

(a) If the rod absorbs 1000 Joules of heat, what is the change in temperature of the rod? Assume copper has a specific heat capacity of 390 J/kg°C and a density of 8,960 kg/m^3.

(b) If the rod is heated until its temperature reaches 100°C, how much heat energy is required? Assume the rod maintains its original dimensions during heating.

Answer:

(a) To determine the change in temperature of the rod, we can use the equation for the heat absorbed or released by an object:

Q=mcΔTQ = mcΔT

Where Q represents the heat energy absorbed or released, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.

First, determine the mass of the rod using its density and dimensions:

Density=mV\text{Density} = \frac{m}{V}

Rearranging the equation gives:

m=Density×Vm = \text{Density} \times V
m=8960 kg/m3×1.5 m×0.008 m2m = 8960 \, \text{kg/m}^3 \times 1.5 \, \text{m} \times 0.008 \, \text{m}^2
m=107.52 kgm = 107.52 \, \text{kg}

Now substitute the given values into the equation:

1000 J=107.52 kg×390 J/kg°C×ΔT1000 \, \text{J} = 107.52 \, \text{kg} \times 390 \, \text{J/kg°C} \times \Delta T

To isolate ΔT, divide both sides of the equation by (107.52 kg)(390 J/kg°C):

ΔT=1000 J(107.52 kg)(390 J/kg°C)\Delta T = \frac{1000 \, \text{J}}{(107.52 \, \text{kg})(390 \, \text{J/kg°C})}
ΔT≈0.233 °C\Delta T \approx 0.233 \, \text{°C}

Therefore, the change in temperature of the copper rod is approximately 0.233°C.

(b) To determine the heat energy required for the rod to reach a temperature of 100°C, we can use the same equation as before:

Q=mcΔTQ = mcΔT

Substituting the given values:

Q=107.52 kg×390 J/kg°C×(100°C−20°C)Q = 107.52 \, \text{kg} \times 390 \, \text{J/kg°C} \times (100°C - 20°C)
Q=107.52 kg×390 J/kg°C×80°CQ = 107.52 \, \text{kg} \times 390 \, \text{J/kg°C} \times 80°C
Q=335,232 JQ = 335,232 \, \text{J}

Therefore, the heat energy required for the copper rod to reach a temperature of 100°C is 335,232 Joules.

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