Answer
$P_{atm}=95.66kPa$
$m(kg)=115.21kg$
Work Step by Step
First we find the pressure make by the mass of the piston:
$F_{p}=mg=5kg*9.81\frac{m}{s^2}=49.05N$
$A_{p}=\frac{\pi*(12cm*\frac{1m}{100cm})^2}{4}=0.0113m^2$
$P_{p}=\frac{49.05N}{0.0113m^2}=4.34kPa$
Then the atmospheric pressure is:
$P_{atm}=P_{abs}-4.34kPa=100kPa-4.34kPa=95.66kPa$
The pressure of the mass will be:
$P_{m}=\frac{m(kg)*9.81\frac{m}{s^2}}{0.0113m^2}=0.868*m(kg)kPa$
If you double the pressure of the gas then the new pressure will be $200kPa$. Then:
$200kPa=P_{atm}+P_{p}+P_{m}=95.66kPa+4.34kPa+0.868*m(kg)kPa$
Solving for $m(kg)$:
$m(kg)=\frac{200kPa-95.66kPa-4.34kPa}{0.868kPa}=115.21kg$
