Problem using Gay-Lussac's law and forces

[lm93]

Homework Statement

A cubic box of volume 4.0 multiplied by 10-2 m3 is filled with air at atmospheric pressure at 20°C. The box is closed and heated to 160°C. What is the net force on each side of the box?

Homework Equations

P1/T1=P2/T2
P=F/A

The Attempt at a Solution

So we can assume that volume is constant because the box is closed. P1=1 atm P2=unknown
T1=20C T2=160C. Using the above equation I got: 1/20=P2/160--> 1/20*160=P2-->P2=8 atm
Then to find the force I thought I should use F=PA. I converted 8 atm into N/m2 and got 810 600N/m2. For the area of one side of the box, I thought that one length of the cubic box was the cube root of 0.04 squared which I found to be 0.11696m2. So then, I put those numbers into the equation and got F=PA--> F=0.11696*810600--> F=94808.35N
But this was wrong

I have tried this problem many different times and keep getting it wrong. I was wondering if it matters the units you use for the first equation P/T=P/T. I thought as long as you kept them constant it didn't...but then when I tried it with different units eg. Kelvins instead of degrees Celsius I got a different answer.

Could someone please help? I would really appreciate it!
Thank you

 

[anathema]

for your post and for showing your attempt at solving the problem. It seems like you have the right idea, but there are a few things that could be causing your incorrect answer.

First, the equation P1/T1 = P2/T2 is known as the ideal gas law, and it is typically used to relate pressure and temperature for a gas in a closed system. In this case, the box is closed, but it is not a closed system since the air can expand and change volume. So, we cannot use this equation to find the pressure of the air inside the box.

Instead, we can use the ideal gas law in conjunction with the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature in Kelvin. Since we know the volume and temperature of the gas before and after heating, we can use this equation to find the final pressure of the gas inside the box.

Second, when converting from atm to N/m2, you should get 810,600 N/m2, not 810,600,000 N/m2. This could be a simple calculation error, but it is important to double check your conversions and units to ensure accuracy.

Lastly, the area of one side of the box should be the surface area, not just one length of the cubic box. Since the box is a cube, all sides have the same area, which can be found by multiplying the length of one side by itself. So, the area of one side should be (0.04 m)^2 = 0.0016 m^2.

With these corrections, your final answer should be around 15,000 N for the net force on each side of the box. I hope this helps and good luck with your studies!

 

[kerimek]

for sharing your attempt at solving this problem. It seems like you have a good understanding of the equations involved, but there may be a few small errors in your calculations.

First, when converting from Celsius to Kelvin, you need to add 273 to your temperature values. So for T1 = 20°C, the corresponding temperature in Kelvin would be 293K, not 20K.

Second, when converting from atm to N/m2, you need to multiply by 101325, not 810600. So your pressure in N/m2 would be 8*101325 = 810600 N/m2.

Third, when calculating the area of one side of the box, you need to use the surface area formula for a cube, which is 6a^2, not the cube root of 0.04 squared. So the area would be 6*(0.04)^2 = 0.0096 m2.

With these corrections, your final answer should be F = 810600 N/m2 * 0.0096 m2 = 7785.6 N.

In general, it is important to pay attention to units and make sure they are consistent throughout your calculations. This can often be a source of errors in problem solving. Additionally, it is always a good idea to double check your calculations and make sure they make sense in the context of the problem. If you are still struggling with this problem, it may be helpful to review the concepts of Gay-Lussac's law and forces, and practice similar problems to build your understanding and confidence. Good luck!