Final answer:
Using the combined gas law, the new pressure of the air inside a smaller box of 5m³ at 35°C is calculated to be approximately 11.75 atm, which is about 12 atm when rounded to two significant figures.
Step-by-step explanation:
To determine the new pressure when the same amount of air is placed in a smaller volume and at a higher temperature, we can use the combined gas law, which is derived from Boyle's, Charles's, and Gay-Lussac's laws:
P1 * V1 / T1 = P2 * V2 / T2
Where:
- P1 is the initial pressure (3.65 atm)
- V1 is the initial volume (15 m³)
- T1 is the initial temperature in Kelvin (25°C = 298.15 K)
- P2 is the final pressure
- V2 is the final volume (5 m³)
- T2 is the final temperature in Kelvin (35°C = 308.15 K)
Substituting the known values into the equation:
3.65 atm * 15 m³ / 298.15 K = P2 * 5 m³ / 308.15 K
Now, solving for P2:
P2 = (3.65 atm * 15 m³ / 298.15 K) * (308.15 K / 5 m³)
P2 = (3.65 * 3) * (308.15 / 298.15)
P2 ≈ 3.65 * 3 * 1.0335
P2 ≈ 11.365 * 1.0335
P2 ≈ 11.75 atm
The new pressure of the air inside the smaller box would be approximately 11.75 atm, rounded to two significant figures, it's 12 atm.