A cubic box of volume 4.2 multiplied by 10-2 m3 is filled with air at atmospheric pressure at 20°C. The box is closed and heated to 195°C. What is the net force on each side of the box?

My attempted solution:
.042^(1/3) = .3476 m for the area
.042^(2/3) = .1208 m for the area of a side
(273 + 195)/(273+20) = 1.597
1.597 * .1208 = .19292
.19292 was my answer.
Did I not take this far enough or is the entire set-up wrong?

Volume = 4.2*10^-2 m^3

Side length is the cube root of that:
a = 0.34760 m
Side area = a^2 = 0.1208 m^2
Absolute Temperature ratio = 1.5973

New atmospheric pressure
= 1.5973*1.013*10^5 N/m^2
= 1.618*10^5 N/m^2

Multiply that by the area of a side.

Your only mistake was not converting pressure from atmospheres to Pascals (N/m^2)

Your attempted solution has some incorrect steps. Let's break down the problem and correct the approach:

1. Calculate the initial volume of the cubic box: 4.2 x 10^(-2) m^3. This is equal to the initial volume when the box is filled with air at atmospheric pressure and 20°C.

2. The box is heated to 195°C. To determine the final volume of the box, we can use the ideal gas law, which states that the volume of a gas is directly proportional to its absolute temperature at constant pressure. However, we need to ensure that the pressure remains constant, which is not explicitly mentioned in the problem. Assuming the pressure remains constant, we can use the following equation:

(V₁ / T₁) = (V₂ / T₂)

Where:
V₁ = initial volume of the box
T₁ = initial temperature of the air
V₂ = final volume of the box (which we need to find)
T₂ = final temperature of the air

Plugging in the given values:
V₁ = 4.2 x 10^(-2) m^3
T₁ = 20°C + 273.15 (to convert to Kelvin)
T₂ = 195°C + 273.15 (to convert to Kelvin)

Now we can solve for V₂:
V₂ = (V₁ x T₂) / T₁

3. Once we find the final volume of the box (V₂), we can calculate the side length (l) of the cube. Since it is cubic, all sides will have the same length. We know that the volume of a cube is given by V = l^3, so:

V₂ = l^3

Rearranging the equation to solve for l:
l = ∛(V₂)

4. Finally, we can calculate the net force on each side of the box using the formula for pressure:

Pressure (P) = Force (F) / Area (A)

Since the box is closed, the pressure inside the box will be equal to the atmospheric pressure. Therefore, we need to calculate the pressure at each temperature and find the force on each side.

The equation for pressure is:

P = (nRT) / V

Where:
n = number of moles of air
R = ideal gas constant
T = temperature in Kelvin
V = volume in cubic meters

We can calculate the pressure at both initial and final temperatures using this equation. And since all sides of the box are equal in area, we can find the net force on each side by multiplying the pressure by the area of one side.

So, to summarize the steps:

1. Calculate the final volume of the box (V₂) by using the ideal gas law.
2. Find the side length of the cube (l) by taking the cube root of V₂.
3. Calculate the pressures (P₁ and P₂) at both temperatures using the equation for pressure.
4. Calculate the net force on each side of the box by multiplying the pressure by the area of one side.

It's important to note that to accurately solve this problem, we need to know the number of moles of air in the box, as well as the value of the ideal gas constant (R).