Net force?

Question

A cubic box of volume 5.3E-2 m3 is filled with air at atmospheric pressure (P = 1.00 atm) at 23°C. The box is closed and heated to 1.70E2°C. What is the net force on each side of the box?

Answer 1

The force on each side of the box will be caused by the increased pressure on the inside of the box due to the thermal expansion of the air inside the box.  Therefore we will need to know the area of each side of the box.

L = V^1/3  (cube root of the volume)

L = 0.376m

A = L^2

A = 0.141m^2

Now we need to use the ideal gas law (PV=nRT) to determine the pressure change given a known temperature change.  Since the ideal gas constant, the number of moles of gas, and the volume are constant, they will be the same before and after the heating.  The ideal gas law rearranged is:

V/(n*R) = Ti/Pi = Tf/Pf

So now you just need to enter the known values and calculate the final pressure (Pf).  (Make sure you remember to convert your temps to Kelvin - 296K to 443K.)

Pf = Pi * Tf/Ti

Pf = 1.5 atm

So the last step is just to convert to some common units and calculate the force that this pressure causes on the calculated area.

F = Pf * A

F = 21,400 N

F = 4,810 lbs force

Answer 2

Let

s = length of the side of a cubic box

Since the volume of the box = 0.053 m^3, then

s^3 = 0.03

s = 0.376 m

Therefore, the area of one side = s^2 = 0.1414 m^2

Since the heating process took place at constant volume, then

(P/T)1 = (P/T)2

where

P and T are pressures and temperatures, respectively & the subscripts 1 and 2 refer to initial and final conditions, respectively.

Since 1 atm = 1,013,250N/m^2

then

P1 = 1,013,250 N/m^2

T1 = 23 + 273 = 295 Kelvin

T2 = 170 + 273 = 443 Kelvin

NOTE:  The temperatures have to be converted to the absolute Kelvin scale before they can be used in this calculation.

Substituting appropriate values and solving for "P2",

P2 = 1,013,250 *443/295

P2 = 1,521,592.37 N/m^2

Since Force = Pressure * Area,

then

F = Force on each side of the box = (1,521,592.37)(0.1414)

F = 215,153.16 Newtons

Answer 3

PV=RT

V stays constant, so new pressure =

                       ((273+new temp)/(273 + 23) )  * original pressure

[is yr new temp 170deg C ?]

Force on side of box = new pressure * area of side

area of side = (cube root of 5.3whatever ) squared