Cycle II AP Physics
John Dewey High School
Mr. Klimetz

Thermal Energy I: Calculation and Relationship to the Total Energy State of an Object

Useful Equations and Concepts
The total energy of a body is equal to the sum of its kinetic, potential and internal (thermal) energies.
The total energy of a closed system is a constant, although there may be conversions of energy from one form into another.
Heat energy always flows from bodies with higher temperature to bodies with lower temperature. Reversing the flow of energy requires that work be done.
Increases in the temperature of an object are associated with an increase in Kinetic Molecular Energy, that is, the rate at which its component atoms and molecules are vibrating.
Changes in a material's phase is associated with changes in its Molecular Potential Energy, that is, the strength of the bond between adjacent atoms and molecules and the overall bond distance.
The heat gained or withdrawn during phase changes is isothermal and is referred to as latent heat.
Specific heat capacity is the temperature response of a unit quantity of a specific type of matter to the gain or withdrawal of a unit value of heat energy.
Heat energy is usually expressed in kilojoules.
The specific heat capacity of liquid water is 4.19 kJ/kg-degC and is the reason why water is a major reservoir of heat energy at the Earth's surface.
A calorimeter is a device designed to preserve the thermal energy of its contents.

Heat Equations
Q = mcp(Tfinal-Tinitial) [for heat gained or withdrawn without an accompanying phase change]

Q = mHf [for heat gained or withdrawn during the solid-liquid phase transition]
Q = mHv [for heat gained or withdrawn during the liquid-vapor phase transition]

Solve the following problems on a separate sheet of paper or in the spaces provided. Remember to use proper problem-solving techniques throughout.

1.  A quantity of heat is added to 5.00 kg of water at 19.0 degrees C such that a final temperature of 179 degrees C is reached. (A) Calculate the amount of heat energy gained by the water. (B) Imagine that all of the heat energy calculated in part (A) is transferred to an automobile's engine without loss. If the total mass of the automobile is 1,500. kg, calculate the net displacement the car can achieve if we neglect friction. [Is this problem solvable?]

2.  A glowing 100.-watt waterproof light bulb is immersed in 300. milliliters of 23.0 degrees C water in a calorimeter. Assuming that there is no loss of heat energy to the outside, calculate (A) the amount of time required to achieve boiling, and (B) the amount of time required to vaporize the entire quantity of water.

3.  Calculate the final temperature of a system consisting of 738 grams of copper at 410 degrees C dropped into a calorimeter filled with 14.2 kilograms of ice at -17 degrees C.

4.   A 3.00 kilogram lead ball with a temperature of 30.0 degrees C is thrown horizontally from the roof of a 180.-meter tall apartment building at a speed of 12.0 meters/second. The ball lands in a full tank of 25.0 degrees C water. The tank is 1.00 meter long, 0.700 meter wide and 5.00 meters high. Assuming that there is neither loss of water nor heat and that air friction is neglected, calculate the final temperature of the water and the ball.

Answers:
1. (A) 1.38 x 10exp4 kJ (B) Unsolvable

2. (A) 968 s (16.1 min) (B) 6,780 s (2 h-8 min-43 s)

3. -13 degreesC

4. 28.3 degreesC