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, we need to calculate the change in volume due to the change in temperature.
First, let's convert the temperatures from Fahrenheit to Celsius using the formula:
°C = (°F - 32) * (5/9)
Initial temperature, Ti = (70 - 32) * (5/9) = 21.11 °C
Final temperature, Tf = (160 - 32) * (5/9) = 71.11 °C
Next, we need to convert the temperatures from Celsius to Kelvin by adding 273.15 to each value:
Ti = 21.11 + 273.15 = 294.26 K
Tf = 71.11 + 273.15 = 344.26 K
Now we can calculate the change in volume using Charles' Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin.
The formula is:
Vf = Vi * (Tf / Ti)
Where:
Vi = initial volume = 400 cubic feet
Tf = final temperature in Kelvin = 344.26 K
Ti = initial temperature in Kelvin = 294.26 K
Vf = 400 * (344.26 / 294.26) = 470.2 cubic feet
Therefore, the volume of air that escapes from the tank is 470.2 cubic feet.