Question

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 ?

Answer 1

$p=const$ 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