Answer to Question #294986 in Physics for Brownies

Question #294986

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?

1
Expert's answer
2022-02-07T15:27:11-0500

Given:

T=t+273=(15.5+273)°C=288.5°CT=t+273=(15.5+273)\rm °C=288.5°C

p=1.72105Pap=1.72* 10^5\rm\: Pa

V=2.81m3V=\rm 2.81\: m^3


(A)

pV=nRTpV=nRT

n=pVRT=1.721052.818.31288.5=202moln=\frac{pV}{RT}=\frac{1.72*10^5*2.81}{8.31*288.5}=202\:\rm mol

(B)

p1V1T1=p2V2T2\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}

p2=p1V1T2V2T1p_2=p_1\frac{V_1T_2}{V_2T_1}

=1.721052.81301.24.16288.5=1.21105Pa=1.72*10^5*\frac{2.81*301.2}{4.16*288.5}=1.21*10^5\:\rm Pa


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