David W. Spitzer

The pressure of a gas increased from 4 bar to 5 bar. Its temperature increased from 25 C to 55 C. Approximately how much was the gas compressed or expanded?

A.    Compressed by 20 percent
B.    Compressed by 10 percent
C.    No change
D.    Expanded by 10 percent
E.    Expanded by 20 percent

Commentary
Boyle’s Law and Charles’ Law can be used to estimate the effects of pressure and temperature on the gas. Atmospheric pressure is estimated to be 1 bar absolute to simplify calculations.

The gas pressure increased from 5 bar absolute (4+1) to 6 bar absolute (5+1).  Per Boyle’s Law, higher pressure tends to compress gases so the gas was compressed by approximately 20 percent (6/5).

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The absolute temperature increased from approximately 300K (25+273) to approximately 330K (55+273), or approximately 10 percent. Per Charles’ Law, higher temperatures tend to expand gases so the gas was expanded by approximately 10 percent (330/300).

The approximate change can be estimated by mathematically adding the individual effects. A 20 percent compression and 10 percent expansion would net a compression of approximately 10 percent, so Answer B would be the best answer.