Assume that you have a cylinder fitted with a movable piston and enclosing a fix

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. 25. A. What would happen to the gas pressure inside the eylinder if youdcrease the volume to one-fourth the original volume while holding the temperature constant ? B. What would happen to the gas volume inside the cylinder if the pressure is doubled and the Kelvin temperature is doubled? 26. Suppose you are given two 1-L flasks (e.g. flasks A and B) and told that one contains a gas of molar mass 30, the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is X atm, and the mass of gas in flask A is 1.2 g. The pressure in flask B is 0.5X atm, and the mass of gas in flask B is also 1.2 g. Which flask contains gas of molar mass 30, and which contains the gas of molar mass 60? Show mathematical proof to explain. Flask A Flask B 1.2 g gas A 1.2 g gas B 12

Explanation / Answer

Ans 25 :

A) Using the ideal gas law , pV = nRT , pressure is inversely proportional to the volume of gas.

p1V1 = p2V2

So here , V2 will be V1/4

putting values :

p1V1 = p2V1/4

p2 = 4p1

So the gas pressure becomes four times.

B) Using the ideal gas law again , we get the relation as :

p1V1T2 = p2V2T1

Now here , p2 = 2p1 and T2 = 2T1

So putting all the values :

p1V1 x 2T1 = 2p1 x V2 x T1

V1 = V2

So the gas volume does not change at all.

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