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Flashcards · AP® Physics 2: Algebra-Based · Unit 9

Unit 9: Thermodynamics flashcards

41 cards on topics 9.1 to 9.6. Pick a topic or study the whole unit.

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9.1 Kinetic Theory of Temperature and Pressure

How does kinetic theory explain gas pressure?
Atoms hit the walls and change momentum. Many tiny impulses each second add up to a steady average force F⊥, and pressure P = F⊥/A. Pressure exists everywhere in the gas, not just at the walls.
What is the momentum change of an atom bouncing elastically off a wall?
Δp = 2mv cos θ, with θ measured from the normal. Only the perpendicular component reverses. Head-on, Δp = 2mv, not mv.
What does temperature measure in kinetic theory?
The average kinetic energy of the atoms: K_avg = (3/2)k_B T = ½m v_rms², with k_B = 1.38 × 10⁻²³ J/K and T in kelvin. A single atom has no temperature.
A gas is heated from 100 K to 900 K. By what factor does v_rms change?
× 3. v_rms = √(3k_B T/m), so v_rms ∝ √T and √9 = 3. Doubling T doubles K_avg but raises v_rms by only √2.
How does the Maxwell–Boltzmann speed distribution change when a gas is heated?
The peak moves to a higher speed, the curve widens and the peak gets lower; the area under it is unchanged. Lighter atoms at the same T show the same shift.
At the same temperature, do heavier gas atoms have more kinetic energy?
No. All atoms at the same T have the same average kinetic energy; heavier atoms simply move more slowly.
What is the average kinetic energy of a gas atom at 400 K?
K_avg = (3/2)k_B T = 1.5 × 1.38 × 10⁻²³ × 400 ≈ 8.28 × 10⁻²¹ J. Always use kelvin, never °C.

9.2 The Ideal Gas Law

What is the ideal gas law?
PV = nRT with P in Pa, V in m³, n in mol, R = 8.31 J/(mol·K), T in K. In terms of atoms: PV = Nk_BT. Pair n with R and N with k_B.
What are the assumptions of the ideal gas model?
Random atomic velocities; atoms' own volume negligible; elastic collisions; no forces on atoms except during collisions. Real gases fit best at low pressure and well above condensation temperature.
A fixed amount of gas has its volume halved and its absolute temperature doubled. How does its pressure change?
P₁V₁/T₁ = P₂V₂/T₂, so P is multiplied by 2 (from T) × 2 (from V) = 4.
Does heating a gas from 20 °C to 40 °C double its pressure at constant volume?
No. Use kelvin: the factor is 313/293 ≈ 1.07. Ratios only work with absolute temperature.
How is absolute zero found from gas data?
Plot P against T in °C at constant volume, draw the best-fit line and extrapolate to P = 0. The intercept is about −273 °C (0 K). It is found by extrapolation, not measurement.
What straight-line graphs test the ideal gas law?
P against 1/V at constant T (gradient nRT); V against T in K at constant P (gradient nR/P); P against T in K at constant V (gradient nR/V). All pass through the origin.
How many moles of ideal gas fill 2.0 L at 1.0 × 10⁵ Pa and 300 K?
n = PV/(RT) = (1.0 × 10⁵ × 2.0 × 10⁻³) / (8.31 × 300) ≈ 0.080 mol. Convert litres to m³ first.

9.3 Thermal Energy Transfer and Equilibrium

What are the three thermal processes?
Conduction: collisions between neighbouring particles (needs matter). Convection: bulk movement of a fluid. Radiation: electromagnetic waves, the only one that can cross a vacuum.
What decides the direction of net energy transfer between two objects in thermal contact?
Temperature, not internal energy. A hot nail dropped into a large tank of cooler water transfers energy to the water, even though the water has more internal energy.
Why does energy usually flow from hot to cold at the atomic scale?
In a collision energy is most likely, but not certain, to pass from the higher-energy atom to the lower-energy one. After very many collisions the most probable state is equal temperatures.
What is thermal equilibrium?
No net energy transfer by thermal processes between systems in contact: they are at the same temperature. Atoms still exchange energy; the net is zero.
How do you find the final temperature when two samples of the same monatomic gas mix energy in rigid insulated boxes?
T_f = (N₁T₁ + N₂T₂)/(N₁ + N₂): weight by the number of atoms. Equal numbers at 300 K and 500 K give 400 K.
Can convection happen in a solid?
No. Convection needs bulk movement of a fluid. Solids transfer energy by conduction (and radiation).

9.4 The First Law of Thermodynamics

What is the first law of thermodynamics?
ΔU = Q + W, where Q is energy transferred into the gas by heating and W is work done on the gas. It is conservation of energy for a closed system.
What is the sign of W for an expanding gas in this course?
Negative. W = −PΔV is the work done on the gas; an expanding gas does work on its surroundings, so W is negative.
A gas is heated with 300 J and does 120 J of work on its surroundings. What is ΔU?
W = −120 J, so ΔU = Q + W = 300 − 120 = +180 J.
What does the first law become for each special process?
Isochoric (constant V): W = 0, ΔU = Q. Isothermal: ΔU = 0, Q = −W. Adiabatic: Q = 0, ΔU = W. Isobaric: Q = (5/2)nRΔT for a monatomic gas.
What is the internal energy of an ideal monatomic gas?
U = (3/2)nRT = (3/2)PV: only the kinetic energy of the atoms, depending only on T (in kelvin). An ideal gas has no internal potential energy.
How do you find work from a PV diagram?
The area under the path gives |W|; the direction gives the sign (expansion: work on gas is negative). Around a closed cycle, ΔU = 0 and |W_net| is the enclosed area.
What is the difference between heat and internal energy?
Internal energy U is a property of the gas. Heating (Q) and work (W) are transfers across the boundary, not contents. A gas has U, not "heat".

9.5 Specific Heat and Thermal Conductivity

What is specific heat?
c is the energy needed to raise 1 kg of a material by 1 K, in J/(kg·K). Q = mcΔT. It is intrinsic: the same for a bead and a block of one material.
Does a material with high specific heat warm up quickly?
No. High c means a slow temperature change for a given energy input.
How do you find a final temperature when objects mix in an insulated container?
Use Σ mcΔT = 0 with signed ΔT. The answer must lie between the starting temperatures; take a simple average only if the mc values are equal.
How do you find c from heater data?
Energy supplied Q = PΔt. The slope of a T against t graph is P/(mc), so c = P/(m × slope). The slope of T against Q is 1/(mc).
What is the rate of conduction through a slab?
Q/Δt = kAΔT/L, with k the thermal conductivity in W/(m·K). Doubling A or ΔT doubles the rate; doubling the thickness L halves it.
Why does a metal bench feel colder than a wooden one at the same temperature?
Metal has a higher thermal conductivity (free electrons), so it conducts energy away from your hand faster. It is not actually colder.
Do you add 273 to a temperature change?
No. A change of 10 °C is a change of 10 K, so ΔT has the same value in either unit.

9.6 Entropy and the Second Law of Thermodynamics

What is entropy?
A measure of how spread out a system's energy is. More spread-out energy means higher entropy and less energy available to do work. Only qualitative reasoning is needed in this course.
What is the second law of thermodynamics?
The total entropy of an isolated system never decreases. It stays constant only if every process is reversible; real processes increase it.
Hot soup cools in a room. What happens to the entropy of the soup, the room and the total?
The soup's entropy decreases, the room's increases by more, and the total increases. A closed system's entropy can fall; the isolated total cannot.
What is the entropy change of a gas over a complete cycle?
Zero. Entropy is a state function, so it depends only on the state. Two paths between the same states give the same ΔS for the system, though Q and W differ.
Does a free expansion with Q = 0 leave entropy unchanged?
No. The gas spreads into a larger volume, so its entropy rises even though Q = 0. It is an irreversible process.
Is it impossible to move energy from cold to hot?
Only spontaneously. A freezer or refrigerator does it using work, and the total entropy still increases.
Which processes are irreversible?
Friction, mixing, free expansion and heating across a temperature difference. A reversible process must be very slow, frictionless and involve no heating across a finite temperature difference.

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