It id desired to increase thr volume of gas by 20% without changing the pressure .To what temperature the gas must be heated if the initial temperature of the gas is 27degree celcius?​

32.4°C

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