Answer to Question #251437 in Molecular Physics | Thermodynamics for Bebe

Question

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? 

Answer 1

$P_1= 101.325\textsf{kPa}\\ T_1 = 16°C = (16+273)\textsf{ K} = 289\textsf{ K}\\ V _1= 2.83\textsf{ m³}\\ P_2= 1171.8\textsf{ kPa}\\ V_2=V_3= 0.31\textsf{ m³}\\ P_3= 137.8 \textsf{ kPa}\\ T_3 = 24°C = (24+273)\textsf{ K} = 297\textsf{ K}$

m of gas to be compressed in the storage vessel

$PV = m_1RT\\m3 = m 2 + m 1$

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

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

for final temperature, T3:

$PV = mRT_3\\ (1171.8)(0.31)= PV/T_3= 1.13604 \\T_3= 319.758°K$