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 ?

Expert's answer

@$p=const@$ 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 @$227°C@$ @$V=8\cdot(227+273)=4000@$ @$m^3@$

@$pV=\frac{m}{M}RT@$

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

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

@$\frac{\rho_1}{\rho_2}=\frac{T_2}{T_1}=\frac{500}{250}=2@$ **Answer**

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