A compartment measures 3.5 meters by 5.5 meters and is 3 meters high. A fire raises the temperature from 68of to 1500 of. If the starting pressure was 1 atmosphere, what volume is present at the elevated temperature assuming the compartment has openings to reduce pressure? For the temperatures, make sure to convert to an Absolute Temperature Scale, Kelvin (or Rankine).
To find the volume at the elevated temperature, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature
We know the initial pressure (P1) is 1 atmosphere, the final temperature (T2) is 1500 °F, and the initial temperature (T1) is 68 °F. We need to convert the temperatures to the absolute temperature scale, Kelvin.
To convert Fahrenheit to Kelvin, we can use the formula:
T(K) = (T(°F) + 459.67) * (5/9)
Converting the temperatures:
T1(K) = (68 + 459.67) * (5/9) = 294.26 K
T2(K) = (1500 + 459.67) * (5/9) = 899.82 K
Now, we can rearrange the ideal gas law equation to solve for V2 (the volume at the elevated temperature):
V2 = (P1 * V1 * T2) / (P2 * T1)
Since the compartment has openings to reduce pressure, we can assume the final pressure (P2) remains at 1 atmosphere.
Plugging in the values:
P1 = 1 atm
V1 = 3.5 m * 5.5 m * 3 m = 57.75 m^3
T1 = 294.26 K
T2 = 899.82 K
P2 = 1 atm
V2 = (1 * 57.75 * 899.82) / (1 * 294.26)
V2 = 165.29 m^3
Therefore, the volume at the elevated temperature is approximately 165.29 cubic meters.