If the pressure of a gas sample is quadrupled and the absolute temperature is doubled, by what factor does the volume of the sample change

The new volume of the sample is halved.

Explanation:

Data obtained from the question include the following:

Initial volume (V1) = V

Initial temperature (T1) = T

Initial pressure (P1) = P

Final pressure (P2) = quadrupled = 4P

Final temperature (T2) = doubled = 2T

Final volume (V2) =?

Thus, we can obtain the new volume of the same by using the combined gas equation as shown below:

P1V1 /T1 = P2V2 /T2

P × V/T = 4P × V2/2T

Cross multiply

T × 4P × V2 = P × V × 2T

Divide both side by T × 4P

V2 = (P × V × 2T) / (T × 4P)

V2 = V/2

V2 = ½V

Therefore, the new volume of the sample is halved .

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