Final answer:
To determine the volume of the gas at a different pressure and temperature using the combined gas law, the initial and final values of pressure, volume, and temperature are needed. By substituting the given values into the combined gas law formula, we can solve for the final volume. In this case, the volume of the gas at 135 K and a pressure of 250 kPa is approximately 3.0375 m³.
Step-by-step explanation:
The given problem can be solved using the combined gas law, which relates the pressure, volume, and temperature of a gas. The formula for the combined gas law is:
P1V1/T1 = P2V2/T2
Where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.
Using the given values:
- Initial volume (V1) = 3.0 m3
- Initial pressure (P1) = 135 kPa
- Initial temperature (T1) = 200 K
- Final pressure (P2) = 250 kPa
- Final temperature (T2) = 135 K
Plug in the values into the formula and solve for the final volume (V2):
P1V1/T1 = P2V2/T2
(135 kPa) (3.0 m3) / (200 K) = (250 kPa) (V2) / (135 K)
Solving for V2, the final volume:
V2 = [(135 kPa) (3.0 m3) / (200 K)] * (135 K) / (250 kPa)
Substituting the given values:
V2 = [(135) (3.0) / (200)] * (135) / (250)
V2 = 3.0375 m3
Therefore, the volume of the gas at 135 K and a pressure of 250 kPa is approximately 3.0375 m3.