Question

A 12 oz can of soda is left in a car on a hot day. In the morning the soda temperature was 60oF with a gauge pressure of 40 psi. What will the gauge pressure be when the soda reaches 90oF (or 363 Kelvin)?

Answer 1

In this case, volume of the can remains constant. The relationship between pressure and temperature at constant volume is given by:

P/T = Constant

Then

`( P_(1) )/( T_(1) ) = ( P_(2) )/( T_(2) )`

Where
P1 = 40 psi
P2 = ?
T1 = 60°F ≈ 289 K
T2 = 90°F ≈ 305 K (note, 363 K is not right)

Substituting;

`P_(2) = ( P_(1) T_(2) )/( T_(1) ) = (40*305)/(289) =42.21 psi`