Question

A natural gas storage tank is a cylinder with a moveable top. The volume of the cylinder can change only as its height changes. Its radius remains fixed. The height of the cylinder is 22.3 m on a day when the temperature is 23 ∘C. The next day the height of the cylinder increases to 23.6 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 as an integer.

Answer 1

First the volume of a cylinder is H**R² since none of the dimensions are given except height (H) we an assume that the change in volume is proportional to the change in the cylinder's height.

Charles's law in it's simplified form should give us the answer:
V = kT where V = volume, k is the gas proportionality constant and T is absolute temperature.
Since k is constant we'll find the ratio of the change in absolute temperature to be the same as the ratio of the change in volume (change in height).

V₂/V₁ = T₂/T₁

=>23.6/22.3 = T₂/(23 + 273): we need absolute temperature so we need to add 273 to convert deg C to deg K

=>23.6/22.3= T₂/296

=>296 x 23.6/22.3 = T₂

=>313.25 =T₂ Absolute Temperature ( in deg K)

=>313.25-273 =40.25⁰C = T₂ in (deg C)