Answer
(a) $2.01\%$
(b) $2.01\%$
Work Step by Step
(a) We know that
$v_{rms}^{\prime}=\sqrt{\frac{3RT^{\prime}}{M}}$
This simplifies to:
$T^{\prime}=\frac{(1.01)^2v_{rms}^2\space M}{3R}$
$\implies T^{\prime}=1.0201T\frac{v_{rms}^2 M}{3R}$
$\implies T^{\prime}=1.0201T$
Now the change in temperature can be determined as
$\Delta T=1.0201T-T=0.0201T$
The increase is
$\%=\frac{(0.020T)}{T}\times 100=2.01\%$
(b) We know that the change in pressure is given as
$\Delta P=1.0201P-P=0.0201P$
The percent increase is:
$\%=\frac{0.0201P}{P}\%100=2.01\%$