Question

Assume that you have a cylinder fitted with a movable piston and enclosing a fixed amount of gas. Provide a mathematical proof to your answer for each of the following cases.
​A. What would happen to the gas pressure inside the cylinder if you decrease the volume to one-fourth the original volume while holding the temperature constant?
​B. What would happen to to the gas volume inside the cylinder if the pressure is doubled and the Kelvin temperature is doubled?

Answer 1

Since there is fixed amount of gas , the number of moles of gas are constant .

Now using the ideal gas law , pV = nRT , where p is pressure , V is volume , n is number of moles , R is universal gas constant and T is temperature

A)

p1 xV1 = p2x V2

Now V2 = V1/4

So ,

p1 xV1 = p2 xV1 /4

p2 = 4 p1

So the gas pressure increases four folds ( quadruples ) when the volume was decreased to one fourth.

B)

p1 xV1x T2 = p2 xV2x T1

Now , p2 = 2p1 and T2 = 2T1

So ,

p1 x V1 x 2T1 = 2p1 x V2 x T1

V1 = V2

So there will be no change in the volume of gas , when pressure and temperature is doubled , it remains same .