A cylinder fitted with a movable piston contains ideal gas at 27°C,pressure 0.50 x 10⁵ Pa and volume 1.25 m³.What will be the final temperature if the gas is compressed to 0.80 m³ and the pressure rises to 0.82 × 10⁵ Pa?

Question

Quizplus · Accepted Answer

Explanation:Using the ideal gas law, PV = nRT, we can find the initial and final temperatures of the gas.Initial state:P1 = 0.50 x 10^5 PaV1 = 1.25 m^3T1 = 27°C = 300 KFinal state:P2 = 0.82 x 10^5 PaV2 = 0.80 m^3T2 = ?Using the ideal gas law, we can write:P1V1/T1 = P2V2/T2Substituting the given values, we get:(0.50 x 10^5 Pa)(1.25 m^3)/300 K = (0.82 x 10^5 Pa)(0.80 m^3)/T2Solving for T2, we get:T2 = 314.6 K = 41.6°CTherefore, the final temperature of the gas is 41.6°C, which is closest to choice A) 41.8°C.

A Cylinder Fitted with a Movable Piston Contains Ideal Gas