A cubic metal box that has 27.8-cm (.278 m) long edges contains air at a pressure of 1.00 atm (~101,300 Pa) and a temperature of 303 K. The box is sealed so that the enclosed volume remains constant, and it is heated to a temperature of 416 K. Find the force due to the internal air pressure on each wall of the box
1. (P1*V1)/T1 = (P2*V2)/T2
2. P = F/A
3. Area of one side = length * width
The Attempt at a Solution
I have no idea why I am not getting the correct answer here... From other sources I've found online, it looks like my methodology is correct.
Since the amount of gas is constant, I used the form of the ideal gas law given in equation 1. Since volume is constant, I canceled it from both sides of the equation, which leaves me with 101300 Pa/303 K = P2/ 416 K, which gives P2 = 139078 Pa. The area of one side is .278^2 = .077284 m^2. Solving for force in equation 2 and plugging in these numbers gives F = 139078 Pa * .07728 m^2 = 10747 N. However, this isn't the right answer.
Did I do something wrong here? This method seems to make sense, but doesn't yield the correct answer.