. An open tank holding 400 cubic foot of air at atmospheric pressure at 70 degrees F and heated to 160 degree F. What is the volume of air that escapes from the tank?
To find the volume of air that escapes from the tank, you will need to consider the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT.
P: Pressure of the gas
V: Volume of the gas
n: Number of moles of gas
R: Ideal gas constant (0.08206 L·atm/(mol·K) for most situations)
T: Temperature of the gas in Kelvin
First, let's convert the given temperatures to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature scale. So, 70 degrees Fahrenheit is equal to (70 - 32) * 5/9 + 273.15 = 294.261 K, and 160 degrees Fahrenheit is equal to (160 - 32) * 5/9 + 273.15 = 422.039 K.
Next, we need to calculate the initial number of moles (n1) and the initial volume (V1) of air in the tank. Since we are given the volume of the air (400 cubic foot) and the atmospheric pressure, we can use the ideal gas law to find the initial number of moles.
P1 = atmospheric pressure = 1 atm
V1 = initial volume = 400 cubic foot
T1 = initial temperature = 294.261 K
Rearranging the ideal gas law equation to solve for n1:
n1 = (P1 * V1) / (R * T1)
Substituting the values:
n1 = (1 atm * 400 cubic foot) / (0.08206 L·atm/(mol·K) * 294.261 K)
Now, we need to calculate the final volume (V2) of air in the tank. Since the final pressure is not given, we will assume it remains constant at atmospheric pressure. So, the final pressure (P2) is also 1 atm.
V2 = final volume (unknown)
T2 = final temperature = 422.039 K
Using the ideal gas law again:
P1 * V1 / T1 = P2 * V2 / T2
Substituting the known values:
1 atm * 400 cubic foot / 294.261 K = 1 atm * V2 / 422.039 K
Solving for V2:
V2 = (1 atm * 400 cubic foot * 422.039 K) / (294.261 K)
Now, to find the volume of air that escapes from the tank, subtract the final volume (V2) from the initial volume (V1):
Volume of air that escapes = V1 - V2
Substitute the calculated values into the equation to find the final answer.