Mathematical routines (MR)
Ideal gas taken around a three-step cycle
- Unit 9
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a circuit diagram, a ray diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 20–25 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.
The question
A sample of an ideal monatomic gas is taken around the cycle A → B → C → A. At state A the pressure is 1.0 × 10⁵ Pa, the volume is 2.0 × 10⁻³ m³ and the temperature is 300 K. In process A → B, the gas expands at constant pressure until its volume is 6.0 × 10⁻³ m³. In process B → C, the volume stays constant while the pressure drops to 0.40 × 10⁵ Pa. In process C → A, the gas is compressed back to state A along a path that is a straight line on a graph of pressure versus volume.
Suggested time: 22 minutes
Your answers are saved in this browser as you type.
Part (a)
2 pointsSketch the cycle on axes of pressure P versus volume V. You can't draw here, so describe the graph you would draw: the axes and their units, the coordinates of states A, B and C, the shape of each process, and the direction of each process.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
2 pointsDerive an expression for the energy Q transferred to the gas by heating during process A → B, in terms of , and .
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
3 pointsCalculate (i) the temperatures at states B and C, (ii) the energy transferred to the gas by heating in process A → B, and (iii) the net work done on the gas during one complete cycle.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
3 pointsDuring process C → A, is energy transferred into the gas or out of the gas by heating? Justify your claim using the first law of thermodynamics.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Checking scoring…
Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.