AP Unit 9 Problems

Find B’s velocity after the atom–atom collision and check that the supplied outcome is elastic.

Find the impulse delivered to the wall by one atom A. If 5.0 × 10²² equivalent collisions occur per second over area 0.040 m², find average pressure.

A student says pressure is zero away from the container walls because no wall is present there. Evaluate the claim.

At 300 K compare their average kinetic energies, rms speeds, and average vector velocities if both samples are at rest macroscopically.

Sketch normalized speed distributions for gas A before and after heating. Describe the peak position, peak height, tail, area, and rms-speed factor.

Find the amount of gas and final pressure. State which quantity lets you use a two-state ratio.

Name the four microscopic assumptions in the ideal model and explain why a crowded gas near condensation may fail this model.

Construct a quantitative P-versus-Celsius graph, find a best-fit equation, and extrapolate its horizontal intercept. Explain why you should not attempt to measure that intercept by actually cooling this real gas until its pressure vanishes.

The same gas is held at one fixed temperature and compressed. Create qualitative sketches of P versus V and P versus 1/V on separate labeled axes, annotate the fixed quantities, and state what physical quantity the linear graph’s slope determines.

Create a table with columns for transfer path, thermal mechanism, how energy is carried, and net direction. Include one example each of conduction, convection, and radiation from the mug situation. Then explain whether two plates separated by vacuum can be in thermal contact.

If 120 J passes from water into the spoon, state the signs of Q for water and spoon. Which way is the spontaneous net transfer, and what determines it?

Explain the statistically expected energy transfer during many interactions. Could a single interaction transfer energy the opposite way?

Describe the most probable final state, its thermal transfer, and the combined system’s energy. Is the final temperature necessarily the arithmetic mean?

Calculate initial U, ΔU, and final T using the AP work convention. Explain why these changes do not require the container to move.

Explain why the ideal monatomic U formula has no potential-energy term. Would the same argument work for a heated solid whose structure changes? Then state the conservation rule for an isolated combined system.

Draw and label both directed PV paths on common axes. Calculate W_on for each and find the shared ΔU from the endpoints.

Find Q for each path and name the fixed-variable process of their vertical and horizontal segments. Then sketch an isotherm through A and explain why its shape is not either full two-segment path. Distinguish a quasistatic isothermal expansion from a quasistatic adiabatic expansion doing nonzero work against external pressure, and state why free expansion into vacuum is a different case.

Calculate each temperature rise. Construct quantitative Q-versus-ΔT lines for both materials on common axes with units and appropriate numerical scales. Plot at least three calculated points on each line, including the origin, and state each slope with units.

A larger sample of A has mass 0.60 kg. Compare its specific heat and sample heat capacity with the original A. Explain what microscopic features influence c and name the AP temperature approximation.

Find energy-transfer rate, direction, and energy transferred in 5.0 minutes. A replacement slab of the same material doubles area, triples thickness, and has half the temperature difference. Predict its rate.

Propose a controlled experiment to compare two materials’ conductivities using slabs. Explain why making one slab thicker does not change its intrinsic conductivity and why a material’s c cannot replace k in the rate equation.

Compare Q, W_on, ΔU, and final temperature. Then determine the qualitative entropy change and explain why it is consistent with conservation of energy.

Why is the equilibrium state described as maximum entropy under these constraints? Could the gas spontaneously return entirely to its original half while the whole system remains isolated? Explain using probability and the second law.

Draw a boundary around the closed block and a larger isolated analysis boundary containing the block and all relevant surroundings. Add an arrow for thermal energy flow and label the qualitative entropy signs for block, surroundings, and isolated total. Use the diagram to explain whether the block’s entropy can decrease and how interactions with surroundings determine its change.

Compare the block’s entropy changes for the two routes and the total entropy changes of block plus all surroundings. Explain what reversible means.

Construct the directed PV cycle. Rank the four gas temperatures and find net W_on, net ΔU, and net Q for one cycle.

Find Q for each segment using U = (3/2)PV. How much total energy enters by heating and leaves by cooling?

A salesperson claims a redesign could cyclically turn energy drawn from one thermal reservoir entirely into stored work, such as raising an ideal weight, with no other net change besides the reservoir’s energy loss and the work store’s energy gain. Evaluate the claim using an isolated boundary containing engine, reservoir, and ideal work store. The first law alone gives no numerical objection. Use qualitative entropy reasoning.

Give a feasible procedure that obtains the required measurements, controls major energy losses, and determines the unknown specific heat. Then calculate c from the trial.

Treat only final temperature as uncertain by ±0.2 °C, keeping the other trial values exact for this estimate. Recalculate c at both endpoints, identify the range, and explain why final-temperature uncertainty matters strongly here. Would unaccounted energy absorbed by the cup tend to make your inferred c too large or too small?

For the idealized insulated metal–water–cup combination, compare total energy and total entropy before and after equilibration. What does equilibrium mean microscopically?

Find the initial thermal-transfer rate. Is using this initial rate times the full interval duration justified if the gas warms? Explain what measurement would support an energy calculation.

Derive a symbolic relation between Q and ΔT for this isobaric ideal monatomic gas. Use the measured 180 J to calculate ΔT, W_on, ΔU, and the rms-speed factor.

Discuss the qualitative entropy changes of the gas, bath, and isolated total including the surroundings needed for the piston. Does the gas’s receipt of energy imply that every system gains entropy?