Answer
A cubic box with a volume of 5.1 x 10-2 m3 is filled with air at atmospheric pressure at 20 degrees C. The box is closed and heated to 180 degrees C. Assume that there is no leakage from the box and that the box is rigid - volume does not change. What is the net force on each side of the box?
Force is pressure times area and, from above, we know the area (one side of the cube)
The net force on each side is the pressure difference between the inside and the outside times the area of a side.
We are given the outside pressure (1 atmosphere)
The net force on each side of the box will be the pressure
difference between the inside and outside of the box, times the area of a
side of the box. The outside
pressure is 1 atmosphere. The
ideal gas law is used to find the pressure inside the box, assuming that the
mass of gas and the volume are constant.
How do we find the
pressure inside the box and complete the solution?
Answer
The mass of the gas will be constant (nothing added to or removed from the box). Also since the box is rigid, the volume remains constant.
Use the ideal gas law
PV = nRT ð P/T = nR/V = constant why, what is the rationale for this relationship?
P2/T2 = P1/T1 ð
P2 = P1T2/T1 = (1.00 atm)(273 +
180)K/(273 + 20)K = 1.55 atm
F = (Delta Pressure)(Area) = 7.6 x 103 N
What is delta pressure?
How do you find the area?