Answer to Question #122214 in Molecular Physics | Thermodynamics for Gopaul

Question

Oxygen O2, at a pressure of 200 bars, will be contained in a steel container at a temperature of 20 oC.
The volume of the container is 0.04 m3. Assuming that O2 is an ideal gas, calculate the mass of O2 which can
be contained in the container.
The container is protected against excessive pressure by a fusible plug which will melt if the temperature
goes too high.
Calculate at what temperature the fuse plug will melt if the pressure is limited to 240 bar.
(The molar mass of oxygen = 32 Kg / Kmol and Ru = 8314 J / Kmol K)

Answer 1

$a)P*V=\dfrac{m}{M}R*T\newline m=\dfrac{PVM}{RT}\newline m=\dfrac{2*10^7*0.4*32}{8314*293}\approx105kg$

$b)a)P*V=\dfrac{m}{M}R*T\newline T=\dfrac{PVM}{Rm}\newline T=\dfrac{24*10^6*0.4*32}{8314*105}\approx352 K=79^oC$