Question

In 1783, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. This balloon, which had a volume of 31 000L at STP, reached an altitude of 1000m, where the pressure was 651 mmHg and the temperature was -9 degrees C. What was the volume, in liters, of the balloon at these conditions?

Answer 1

We know that PV = nRT

Where

T = Temperature ;P = pressure ; n = No . of moles ;R = gas constant ; V= Volume of the gas

As the gas remains the same , n will constant

So PV / T = constant

Thereby PV/T = P'V'/T'

Where

P = initial pressure = 1 atm = 760 mm Hg

V = initial volume = 31000 L

T = initial temperature = 273 K

P'= final pressure = 651 mm Hg

V' = final volume = ?

T' = final temperature = -9 oC = -9+273 = 264 K

Plug the values we get V' = (PVT')/(TP')

                                      = (760x31000x264)/(273x651)

                                     = 34997 L

Therefore the volume of the ballon is 34997 L