A 670-kg meteoroid happens to be composed of aluminum. When...

A $670-\mathrm{kg}$ meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is $-15.0^{\circ} \mathrm{C}$ and it moves at $14.0 \mathrm{km} / \mathrm{s}$ relative to the planet. As it crashes into the Earth, assume the internal energy transformed from the mechanical energy of the meteoroid- Earth system is shared equally between the meteoroid and the Earth and all the material of the meteoroid rises momentarily to the same final temperature. Find this temperature. Assume the specific heat of liquid and of gaseous aluminum is $1170 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}.$

Key Concepts

Energy Conservation

This concept involves the principle that energy cannot be created or destroyed, only transformed from one form to another. In the meteoroid problem, the kinetic energy due to its high-speed motion is converted into thermal energy upon impact, demonstrating the conservation of energy in a closed system.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, usually expressed as one-half the product of its mass and the square of its velocity. This energy becomes the source that, when transformed during impact, contributes to raising the temperature of the meteoroid.

Energy Partitioning

Energy partitioning refers to the principle of how energy is distributed among different components of a system during a transformation process. In this scenario, it is assumed that the energy transformed during the collision is split equally between the meteoroid and the Earth, which affects the resulting temperature increase of the meteoroid.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of heat required to raise the temperature of a unit mass by one degree Celsius. It is crucial in determining the temperature change when a known amount of energy is absorbed by the material.

Temperature Change Calculation

This concept involves using the relationship between the absorbed heat energy, mass, and specific heat capacity to calculate the change in temperature. The formula, ?T = Q/(m·c), where Q is the energy absorbed, m is the mass, and c is the specific heat capacity, is used to determine the final temperature of the meteoroid after energy absorption.

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