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- Homework Statement
- ##30g## of ##O_2## are inside a cylinder with a radius of ##0.1 m## and a height of ##0.7 m## at a temperature of ##20^{\circ}C##. Calculate the gas pressure. Oxygen is added until the pressure increases by ##80\%## compared to the initial one. Calculate the final temperature and the amount of oxygen introduced into the cylinder.

- Relevant Equations
- ##PV=nRT##

The volume of the cylinder is ##V=\pi r^2 h=\frac{7\pi}{250}\ m^3## the number of moles is ##n=\frac{15}{16}\ mol## so from ##PV=nRT## we get ##P=\frac{nRT}{V}=25975.5\ Pa##.

Now, for the second question, it should be an isochoric process so ##V_2=V_1## and ##P_2=P_1+0.8P_1=\frac{9}{5}P_1## and from these, using the ideal gas law, I get ##n_1T_1=\frac{5}{9}n_2P_2## but I have two variables (##n_2## and ##T_2##) so I don't see how I could solve this and I would thus appreciate an hint about how to go forward, thanks.

Now, for the second question, it should be an isochoric process so ##V_2=V_1## and ##P_2=P_1+0.8P_1=\frac{9}{5}P_1## and from these, using the ideal gas law, I get ##n_1T_1=\frac{5}{9}n_2P_2## but I have two variables (##n_2## and ##T_2##) so I don't see how I could solve this and I would thus appreciate an hint about how to go forward, thanks.