Pressure, Temperature, and a Sealed Syringe
Students trap air in a sealed 60 mL syringe, hold the temperature constant, and compress it while recording pressure and volume. Their data give P·V values of 1.02, 1.01, 1.00, 0.99, and 0.97 (arbitrary units) as volume falls from 60 mL to 20 mL. A second part of the practical asks them to explain why a bicycle pump gets hot when used rapidly. One student writes: "The gas gets hot because the pressure increases - pressure causes temperature." Another says the temperature rise is simply friction in the pump barrel. The teacher wants the class to separate the isothermal data from the adiabatic process.
1. Assess whether the syringe data support Boyle's law. Compute the mean P·V and comment on the trend, then explain what the small downward drift suggests physically.
Read the worked answer
Mean P·V = (1.02 + 1.01 + 1.00 + 0.99 + 0.97)/5 = 4.99/5 = 0.998.
Trend: the values fall monotonically by about 5% across the compression. For Boyle's law, P·V should be constant. The scatter is small, so the data are broadly consistent with an inverse relationship - but the systematic downward drift is the interesting feature, not noise (noise would fluctuate around a mean, not trend).
Physical interpretation:
- A steady decline in P·V at fixed nominal temperature means the gas is being cooled slightly as it is compressed - or, more likely, the compression is fast enough that heat is being lost to the syringe walls and surroundings, so T falls.
- Alternatively, the "sealed" volume includes dead space in the tubing and gauge, so the true gas volume is V + V₀ with V₀ > 0. Then P(V + V₀) = constant, and plotting P against 1/(V + V₀) would straighten the data while P·V drifts.
Conclusion to teach: the data are approximately isothermal but not perfectly so. A good answer names the dead-space correction as the first thing to check, because it is a systematic error in the apparatus rather than a thermodynamic effect - and it would produce exactly this kind of smooth drift.
2. Evaluate the two students' explanations of the warming pump, and state what the gas law actually says.
Read the worked answer
Student 1 ("pressure causes temperature"): correctly notices that P and T rise together but reverses the causality and omits the mechanism. In the ideal gas law, P, V, and T are related by PV = nRT - none "causes" the others; a change in one constrains the others given the process. The physical driver here is work done on the gas.
Student 2 ("friction in the barrel"): friction is real and contributes some heating, but it is not the main effect. If it were, an ideal frictionless pump would stay cool - it does not. The dominant effect is adiabatic compression: work done on the gas raises its internal energy, and because the process is too fast for heat to escape (Q ≈ 0), the temperature rises.
What the gas law says: for an adiabatic compression of an ideal gas, TV^(γ−1) = constant and PV^γ = constant, so reducing V raises both P and T. The temperature rise is a consequence of work done on the gas, not of pressure per se.
Contrast with the syringe data: in the slow syringe experiment, heat escapes and T stays roughly constant (isothermal, PV ≈ constant). In the fast pump, heat cannot escape (adiabatic). The two parts of the practical are the same physics under different constraints - a good discussion question is: "What single assumption differs between the two experiments?"