Michael S. answered • 14d
B.S. in Chemistry, Indiana University; Organic Chem Teaching Intern
V1/V2 = 0.622 — that is, about 1 : 1.61. The gas expands to roughly 1.6 times its original volume.
Charles's law (pressure and amount held constant):
V1/T1 = V2/T2 → V1/V2 = T1/T2
Convert to kelvin first
T1 = 245 + 273.15 = 518.15 K
T2 = 560 + 273.15 = 833.15 K
V1/V2 = 518.15 / 833.15 = 0.622
Why kelvin is not optional here
This is the clearest possible illustration. Using Celsius gives 245/560 = 0.438 — a 30% error, and no warning that anything is wrong. The answer looks perfectly reasonable.
The reason is that Charles's law is a statement of proportionality: volume is proportional to absolute temperature. That only holds on a scale whose zero is a true zero — where no thermal energy means no volume. Celsius zero is just the freezing point of water, an arbitrary marker, so ratios of Celsius temperatures are physically meaningless.
A quick way to see it: 0 °C and 100 °C would give a ratio of 0, implying the gas has no volume at freezing. In kelvin the same pair is 273/373 = 0.73 — a modest expansion, which is what actually happens.
Reading the question carefully
It asks for initial to final. Since the gas was heated, it expanded, so this ratio must be less than 1 — and 0.622 is. Had it asked final-to-initial, the answer would be 833.15/518.15 = 1.61. Both are correct numbers to the same physical situation; only one answers what was asked. Getting 1.61 when 0.622 was wanted is the most common way to lose the mark here.
Also note the figure is not needed — no dimensions or pressures enter a ratio problem like this one.
The physical point: that 61% expansion against a constant external pressure is exactly the useful work the question mentions. It is the operating principle of an internal combustion engine — heat the gas, let it push the piston out at constant pressure, extract w = PΔV.
