To solve this problem, you need to use the ideal gas law equation, which is pV = nRT. This equation relates the pressure (p), volume (V), number of moles (n), gas constant (R), and temperature (T).
In this problem, the initial conditions are given as follows:
- Initial pressure (p1) = 1.50 * 10^6 Pa
- Initial volume (V1) = 0.025 m^3
- Temperature (T) = 200 °C (convert this to Kelvin)
To find the final volume (V2), we need to rearrange the ideal gas law equation as follows:
p1V1 = nRT
p2V2 = nRT
Since the number of moles (n) and temperature (T) remain constant throughout the process, we can equate the two equations:
p1V1 = p2V2
Now we can solve for V2:
V2 = (p1V1) / p2
Substituting the given values:
V2 = (1.50 * 10^6 Pa * 0.025 m^3) / (0.95 * 10^6 Pa)
Now, calculate the final volume V2 using a calculator:
V2 = 0.039 m^3
So, the final volume of the container is 0.039 m^3.