A cylinder contains 60 cu in of gas at a pressure of 160 psi. If the piston is compressed so the volume becomes 50 cu in (at a constant temperature), what is the new pressure?

P1V1 = P2V2 (Boyle's Law) - Temperature Constant

Question

A cylinder contains 60 cu in of gas at a pressure of 160 psi. If the piston is compressed so the volume becomes 50 cu in (at a constant temperature), what is the new pressure?

P1V1 = P2V2  (Boyle's Law)  - Temperature Constant

BlackTom AI · Accepted Answer

Boyle's law (P1V1 = P2V2) applies because the temperature is held constant, so pressure and volume are inversely proportional.

1. Relevant knowledge points and concepts
- Boyle's law: For a fixed amount of gas at constant temperature, P · V = constant. Hence P1V1 = P2V2.
- Units for pressure and volume must be consistent; here psi and cubic inches are consistent for the ratio calculation.

2. Complete reasoning process (step by step)
- Identify given values: P1 = 160 psi, V1 = 60 cu in, V2 = 50 cu in.
- Use Boyle's law to solve for P2: P2 = (P1 · V1) / V2.

3. Calculations with intermediate steps
- Compute the numerator: P1 · V1 = 160 psi · 60 cu in = 9,600 (psi·cu in).
- Divide by V2: P2 = 9,600 / 50 = 192 psi.
- Alternate arithmetic view: 160 × (60/50) = 160 × 1.2 = 192 psi.

4. Why the correct answer is correct
- Because temperature is constant, pressure increases in inverse proportion to the decrease in volume. Reducing volume from 60 to 50 cu in is a factor of 50/60 = 5/6 in volume, so pressure increases by the reciprocal 6/5 = 1.2. Multiplying 160 psi by 1.2 yields 192 psi, matching the Boyle’s law calculation.

5. Why the other options are incorrect
- 172 psi: does not come from the correct ratio; no simple factor from 160 yields 172 under Boyle’s law for these volumes.
- 200 psi: would result if V2 were 48 cu in (160 × 60 / 48 = 200), not 50 cu in.
- 180 psi: would correspond to a different volume change (e.g., 160 × 60 / 180 = 53.33 cu in), not the given 50 cu in.

6. Conclusion
- The correct new pressure is 192 psi, which matches the provided answer.

A cylinder contains 60 cu in of gas at a pressure of 160 psi. If the piston is compressed so the volume becomes 50 cu in (at a constant temperature), what is the new pressure? P1V1 = P2V2 (Boyle's Law) - Temperature Constant单项选择题

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