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Chapter 5: Problem 25

A piece of aluminum and a piece of iron fall without air resistance from the top of a building and stick into the ground on impact. Will their temperatures change by the same amount? Explain.

Short Answer

Expert verified
Answer: No, the temperatures of the aluminum and iron pieces will not change by the same amount, as their temperature changes depend on their masses and specific heat capacities, which are different for each material.

Step by step solution

01

Determine the Potential Energy at the Top of the Building

First, find the potential energy stored in both aluminum and iron pieces at the top of the building. The potential energy is given by the formula: PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height of the building.
02

Determine the Kinetic Energy Just Before Impact

As the objects fall, they gain kinetic energy while losing potential energy, since there is no air resistance. Just before the impact, the gained kinetic energy is equal to the potential energy at the top of the building. Thus, KE = PE.
03

Determine the Energy Gained During the Collision

When the objects collide with the ground, they experience an inelastic collision, meaning they stick together and lose kinetic energy. The energy gained upon impact will depend on the mass and specific heat capacity (c) of each material. The specific heat capacity of aluminum is approximately 900 J/kg·K, while the specific heat capacity of iron is approximately 450 J/kg·K.
04

Determine the Temperature Change

The energy gained upon impact is converted to thermal energy, leading to a temperature change in both materials. The formula for temperature change is given by ΔT = Q / (mc), where ΔT is the temperature change, Q is the energy gained, m is the mass, and c is the specific heat capacity of the material.
05

Comparing the Temperature Changes

According to the formula for temperature change, the temperature change depends on the energy gained, the mass, and the specific heat capacity of the material. Since the energy gained depends on mass and specific heat capacity, the final temperature changes for each material will likely be different. In conclusion, the temperatures of the aluminum and iron pieces will not change by the same amount, as their temperature changes depend on their masses and specific heat capacities, which are different for each material.

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Most popular questions from this chapter

Air molecules in a warm room \(\left(27^{\circ} \mathrm{C}=300 \mathrm{~K}\right)\) typically have speeds of about \(500 \mathrm{~m} / \mathrm{s}(1,100 \mathrm{mph})\). Why is it that we are unaware of these fast- moving particles continuously colliding with our bodies?

On a cool night with no wind, people facing a campfire feel a breeze on their backs. Why?

When trying to predict the lowest temperature that will be reached overnight, forecasters pay close attention to the dew-point temperature. Why is the air temperature unlikely to drop much below the dew point? (The high latent heat of vaporization of water is important.)

In Example \(5.3\), is it really necessary to know the mass of the concrete block to solve this problem? Put another way, would the answer be different if it was a 10 -kg block that was dropped instead of a 5 -kg one?

A 1 -kg piece of iron is heated to \(100^{\circ} \mathrm{C}\), and then submerged in \(1 \mathrm{~kg}\) of water initially at \(0^{\circ} \mathrm{C}\). The iron cools and the water warms until they are at the same temperature (in thermal equilibrium). Assuming there is no other transfer of heat involved, is the final temperature closer to \(0^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C}\), or \(100^{\circ} \mathrm{C} ?\) Why?
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