Question

Assume all temperatures to be exact, and neglect significant figures for small changes in dimension. An ideal gas in a cylinder is at 11?C and 4.0atm . If it is heated so its rms speed increases by 20{\rm \\%} , what is its new pressure?

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

Assume all temperatures to be exact, and neglect significant figures for small changes in dimension.
An ideal gas in a cylinder is at 12 degrees C and 2.0atm .
If it is heated so its rms speed increases by 25% , what is its new pressure?

Given that the intial temperature is T1=12 deg =285 K

                       intial pressure is 2.0 atm

   from the defnition of rms speed it is clear that velocity is directly preportional to square root temperature

if v1 is the intial rms speed then the new rms speed is 1.25 times v1

if T2 is the temperature of the gas at this rms speed then

v1/v2=?T1/T2

   1/1.25=?285/T2

  

?285/T2=0.8

   285/T2=0.64

   T2/285=1.5625

   T2=445.3125 K

if P2 is the new preesure then from ideal gas equation

   P2/P1=T2/T1

    P2=T2/T1 x P1

        =3.125 atm