AP Physics 2 - Thermodynamics Unit 9 Notes
Ideal Gases
Ideal gases adhere to specific rules:
Particles are in random, constant motion.
The combined volume of particles is negligible.
Particles exert no forces on each other.
Collisions are elastic.
Average kinetic energy is proportional to temperature.
Ideal Gas Law
The ideal gas law relates pressure, volume, amount of gas, and temperature.
Formula: , where:
P = Pressure (atm, Pascals, mm Hg)
V = Volume (liters)
n = Amount of gas (moles)
R = Ideal gas constant
T = Temperature (Kelvin)
Relationships Derived from the Ideal Gas Law
Boyle's Law
Pressure and volume are inversely proportional:
Example: In a piston, as pressure increases, volume decreases (if no other work is done).
Gay-Lussac's Law
Pressure and temperature are directly proportional:
Example: In a piston, if temperature increases, pressure increases (if all else is constant).
Charles's Law
Volume and temperature are directly proportional:
Example: In a piston, if temperature increases, volume increases (if pressure and moles stay constant).
PV Diagrams
Visual representation of pressure and volume changes.
Pressure (P) on the y-axis.
Volume (V) on the x-axis.
Work Done
The area under the curve represents the work done by or on the gas.
Formula: W = -P\DeltaV
Negative sign indicates work done by the gas; positive indicates work done on the gas.
Work is only done when the volume changes ($\Delta V \neq 0U = Q - WU = Q + W\Delta V = 0.
Isothermal
Temperature remains constant.
Graphically represented as an inverse rational curve (hyperbola).
Internal energy change ($\Delta U$) is zero in this case because temperature is constant.
Adiabatic
No heat is added or removed from the system (Q = 0).
Graph looks similar to isothermal, but the curve is steeper.
Second Law of Thermodynamics
Heat spontaneously flows from a hotter body to a colder body.
Heat transfer is represented by Q:
Positive Q indicates heat added.
Negative Q indicates heat removed.
Equation for heat transfer: Q = mc\Delta T$$, where:
m = mass of the object.
c = Specific heat capacity (depends on the material).
$\Delta T$ = Change in temperature (Tfinal - Tinitial).
Entropy
Entropy (S) is the measure of disorder in a system.
The second law also states that the entropy in an isolated system always increases.
Heating an object increases entropy as molecules move faster and more randomly.
Example: A cup of coffee cools, heat disperses into the air, and the total entropy of the air-coffee system increases.
Entropy cannot be reversed in a closed system.
Entropy can decrease locally if it is accompanied by an increase in entropy in the surroundings.
AP Physics 2: Circuits Review
Ohm's Law
V = IR - Voltage (V), current (I), and resistance (R) are related.
- Increasing resistance decreases current (if voltage is constant).
Series Circuits
- The current condition is the same for all components.
- Total resistance: R_eq = R1 + R2 + ...
- Voltage divides among components.
Parallel Circuits
- Voltage is the same across each branch.
- Total resistance: 1/R_eq = 1/R1 + 1/R2 + ... -
Current divides among branches.
Power
P = IV = I^2R = V^2/R
- Measures energy used per second (Watts).
- Useful for ranking the brightness of bulbs.
Capacitors
- In series: 1/C_eq = 1/C1 + 1/C2 + ...
- In parallel: C_eq = C1 + C2 + ...
- Stored energy: U = 1/2 C V^2
Kirchhoff's Laws
- Junction Rule: Current in = current out.
- Loop Rule: The Sum of voltage changes = 0 around a closed loop.
RC Circuits (Charging/Discharging Capacitors)
- Charging: Q(t) = Q_max(1 - e^(-t/RC)) V(t) = V_max(1 - e^(-t/RC)) -
Discharging: Q(t) = Q0 e^(-t/RC) I(t) = I0 e^(-t/RC) - tau = RC is the time constant.