Question #251437

A certain gas at 101.325 kPa and 16°C whose volume is 2.83 m³ are compressed into a storage vessel of 0.31 m³ capacity. Before admission, the storage vessel contained the gas at a pressure and temperature of 137.8 kPa and 24°C; after admission the pressure has increased to 1171.8 kPa. What should be the final temperature of the gas in the vessel in Kelvin? 


1
Expert's answer
2021-10-19T15:13:45-0400

P1=101.325kPaT1=16°C=(16+273) K=289 KV1=2.83 P2=1171.8 kPaV2=V3=0.31 P3=137.8 kPaT3=24°C=(24+273) K=297 KP_1= 101.325\textsf{kPa}\\ T_1 = 16°C = (16+273)\textsf{ K} = 289\textsf{ K}\\ V _1= 2.83\textsf{ m³}\\ P_2= 1171.8\textsf{ kPa}\\ V_2=V_3= 0.31\textsf{ m³}\\ P_3= 137.8 \textsf{ kPa}\\ T_3 = 24°C = (24+273)\textsf{ K} = 297\textsf{ K}


m of gas to be compressed in the storage vessel

PV=m1RTm3=m2+m1PV = m_1RT\\m3 = m 2 + m 1


(101.325)(2.83)=mR(16+273)(101.325)(2.83)= m R(16+ 273)

m of gas in storage(m1)=0.99221/R(m_1 )= 0.99221/R


for final temperature, T3:

PV=mRT3(1171.8)(0.31)=PV/T3=1.13604T3=319.758°KPV = mRT_3\\ (1171.8)(0.31)= PV/T_3= 1.13604 \\T_3= 319.758°K

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