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Question

A cylinder fitted with a movable piston contains ideal gas at 27°C, pressure  and volume  What will be the final temperature, in degree Celsius, if the gas is compressed to 1m³ and the pressure rises to 1.17 x 10⁵ Pa.

Answer 1

Since the ideal gas is confined in the cylinder, the number of moles doesn't change. So, the ideal gas equation can be written P1V1 = n R T1 or n = P1V1 / RT1 for the initial state. Similarly for the second state, n = P2V2 / RT2. So, P1V1 / RT1 = P2V2 / RT2 and R can be cancelled out giving P1V1 / T1 = P2V2 / T2. As P1, V1, T1, P2, V2 are known, T2 can be calculated.

Important: remember to use degrees Kelvin for the calculation and change T2 back to degrees Celsius in the answer.