Answer
The new pressure of the gas is $1.62~atm$
Work Step by Step
We can find an expression for $v_0$:
$\overline{KE} = \frac{3}{2}~k~T$
$\frac{1}{2}m~v_0^2 = \frac{3}{2}~k~T$
$v_0 = \sqrt{\frac{3~k~T}{m}}$
$v_0 = \sqrt{\frac{3~P~V}{N~m}}$
We can find the new pressure when the rms speed is $0.90~v_0$:
$0.90~v_0 = 0.90~\sqrt{\frac{3~P~V}{N~m}}$
$0.90~v_0 = \sqrt{\frac{3~(0.90)^2~P~V}{N~m}}$
$0.90~v_0 = \sqrt{\frac{3~(0.81~P)~V}{N~m}}$
We can find the new pressure of the gas:
$0.81~P = (0.81)(2.0~atm) = 1.62~atm$
The new pressure of the gas is $1.62~atm$.
