Answer to Question #294986 in Physics for Brownies

Question

An ideal gas at 15.5 °C and a pressure of 1.72 x 10 ⁵pa occupies a volume of 2.81 cubic meter (show solution).

A) How many moles of gas are present?

B) If the volume is raised to 4.16m³, and the temperature raised to 28.2°C, what will be the pressure of the gas?

Answer 1

Given:

$T=t+273=(15.5+273)\rm °C=288.5°C$

$p=1.72* 10^5\rm\: Pa$

$V=\rm 2.81\: m^3$

(A)

$$pV=nRT$$

$$n=\frac{pV}{RT}=\frac{1.72*10^5*2.81}{8.31*288.5}=202\:\rm mol$$

(B)

$$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}$$

$$p_2=p_1\frac{V_1T_2}{V_2T_1}$$

$$=1.72*10^5*\frac{2.81*301.2}{4.16*288.5}=1.21*10^5\:\rm Pa$$