Answer to Question #106649 in Molecular Physics | Thermodynamics for Benita Ukaegbu

Question #106649
There is 2 * 10 ^ 3 m ^ 3 of gas inside a cylindrical vessel with movable piston. The gas temperature is -23 Celsius degrees. The temperature is increased to 227 Celsius degrees with constant pressure. What is the dependence of gas's volume as a function of its temperature? How many times the gas density at lower temperature is bigger than the gas density at higher temperature ?
1
Expert's answer
2020-03-26T12:18:03-0400

"p=const" The process is isobaric. So,


"\\frac{V_1}{T_1}=\\frac{V_2}{T_2}=...=const" "\\to" "V=const\\cdot T"


"const=\\frac{V_1}{T_1}=\\frac{2000}{-23+273}=8" "m^3\/K"


"V=const\\cdot T=8T" Answer


At "227\u00b0C" "V=8\\cdot(227+273)=4000" "m^3"


"pV=\\frac{m}{M}RT"


"p=\\frac{m}{V_1\\cdot M}RT_1=\\frac{\\rho_1}{M}RT_1"


"p=\\frac{m}{V_2\\cdot M}RT_2=\\frac{\\rho_2}{M}RT_2"


"\\frac{\\rho_1}{\\rho_2}=\\frac{T_2}{T_1}=\\frac{500}{250}=2" Answer











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