Exam Review Notes
Heating and Cooling (Chapter 6)
Mixing Equal Masses of Water in a Calorimeter
Experiment: Mixing equal masses of cool water with equal masses of warm water.
Observation: The temperature decrease of the warm water equals the temperature increase of the cool water, given equal masses.
Unequal Masses:
If there's twice as much warm water as cool water, the warm water cools down by half the temperature the cool water raises.
Generalization: If there's n times as much warm water, it cools down by \frac{1}{n} the temperature the cool water raises.
Warm Metal in Equal Mass of Water
Experiment: Placing a warm piece of metal in an equal mass of water.
Observation: The metal's temperature changes much more than the water's.
Specific Heat
Definition: The amount of energy needed to raise the temperature of one gram of a substance by one degree Celsius.
Water's Specific Heat: Water has a much higher specific heat than most substances (except tin).
4.18 \frac{\text{Joules}}{\text{gram} \cdot \degree\text{C}}
Solid water has a different specific heat.
Thermal Energy Transfer in a Calorimeter
Key Concept: Thermal energy lost by the warmer substance equals the thermal energy gained by the colder substance.
Temperature Change: Temperature change isn't always the same when mixing warm and cold substances.
Heating a Substance Without a Phase Change
Thermal Energy Equation: Q = mc\Delta T, where:
Q is the thermal energy.
m is the mass.
c is the specific heat.
\Delta T is the change in temperature.
Units: Ensure units are consistent.
Phase Changes
Definition: Change from one state of matter to another (solid, liquid, gas).
Heat of Fusion: Energy change during solid-liquid phase changes.
thE = mass * heat of fusion
Heat of Vaporization: Energy change during liquid-gas phase changes.
thE = mass * heat of vaporization
Ratio of Temperature Changes
Equal Masses: If 50g of warm water mixes with 50g of cool water, the ratio of temperature decrease to increase is 1:1.
Unequal Masses: If there is twice as much warm water, the ratio of temperature change (warm:cool) is 1:2.
Temperature Change vs. Thermal Energy Change
Example: A large box of water bottles and a single water bottle are both brought inside from the cold.
Temperature Change: Both will experience the same temperature change as they warm to room temperature.
Thermal Energy Change: The smaller water bottle requires less thermal energy due to its smaller mass.
Thermal Energy Equation: Q = mc\Delta T
Specific Heat (Revisited)
Definition: The amount of thermal energy needed to raise the temperature of one gram of a substance by one degree Celsius.
Heat of Fusion (Revisited)
Definition: The amount of energy needed to change one gram of a solid to one gram of liquid.
Units: Measured in joules per gram (\frac{J}{g}).
Melting Point
Definition: The temperature at which a substance changes from solid to liquid.
Comparing Heats of Fusion: When comparing heats of fusion at melting points, focus solely on the energy required for the phase change, not the energy required to reach the melting point.
Energy Skate Park (Chapter 7)
Kinetic and Potential Energy Conversion
Scenario: A pendulum swinging (similar to the energy skate park).
Gravitational Potential Energy (GPE):
Greatest at the highest points of the swing (positions 1 and 5).
Least at the lowest point (position 3).
Kinetic Energy (KE):
Greatest at the lowest point (position 3), where the pendulum is moving fastest.
As the pendulum swings down, GPE converts to KE; as it swings up, KE converts to GPE.
Conservation of Energy
Energy is always conserved but may be transferred from one form to another (e.g., GPE to KE).
Any difference between initial GPE and final KE is due to energy loss as heat.
Distance and Speed
Key Concepts
Moving Forward/Away: Direction of movement.
Constant Speed and Slow Speed: Represented on a graph.
Steepness of Slope: Indicates speed.
Vectors
Vectors
Vectors in Different Directions