Answer:
32.4°C
Step-by-step explanation:
Consider the following expression:
P•V/T =P'•V'/T'
Where P and P' are respectively the initial and the final pressure, V and V's are respectively initial and final volume, and T and T' are respectively initial and final temperature.
We know that the pressure cannot change, so it means that P = P'
We also know that the volume must be increased in 20%, and if we multiply the volume by 1.2 is like increase it in 20%, so we can write that V' = 1.2•V, and changing a little more we can write that V'/V = 1.2
So let's do some maths:
P•V/T = P'•V'/T'
T'•P•V/T = P'•V'
T'•P•V = P'•V'•T
T'=P'•V'•T/P•V
We know that P'=P so the division is equal to 1:
T'= 1•V'•T/V
We also know that V'/V = 1.2, so:
T' = 1.2•T
And we know the value of T, it's 27, so now we just have to solve it:
T' = 1.2•27
T' = 32.4°C