Question

A natural gas storage tank is a cylinder with a moveable top whose volume can change only as its height changes. Its radius remains fixed. The height of the cylinder is 22.8 m on a day when the temperature is 23 ∘C. The next day the height of the cylinder increases to 23.4 m as the gas expands because of a heat wave. Find the temperature, assuming that the pressure and amount of gas in the storage tank have not changed. Express your answer using two significant figures. T=__________∘C

Answer 1

Volume cylinder = r² h

where r = radius of cylinder

h = height of cylinder

Now Initial volume at 22.8m height = r² *22.8

Final volume at 23.4m height = r² *23.4

Now applying   P1V1 / T1 = P2V2 / T2

P1 = Initial pressure = P2 = Final pressure

V1 = Intial Volume , V2 = Final volume

T1 = Initial Temperature = 273+23 = 296K , T2 = Fianl Temperature = ?

As the pressure remains constant, V1 / T1 = V2 / T2

r² *22.8 / 296 = r² *23.4 / T2

T2 = (23.4 * 296) / 22.8 = 303.7894K or 30.7894^oC