Moles & Ideal Gas: Force at 24.0 & 108 C

[ryaneye]

Homework Statement

Three moles of ideal gas are in a rigid cubical box with sides of length 0.380 m.

Homework Equations

What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 24.0 C?
What is the force when the temperature of the gas is increased to 108 C?

The Attempt at a Solution

 

[mgb_phys]

pv = nRT tells you everything you need to know about ideal gases.
You might want to look it up.

 

[baba89]

To calculate the force exerted by the gas on each side of the box, we can use the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin. We can rearrange this equation to solve for pressure: P = (nRT)/V.

First, let's convert the temperature to Kelvin by adding 273.15 to 24.0 C, giving us 297.15 K. Plugging in the values of n = 3 moles, V = (0.380 m)^3 = 0.0546 m^3, and R = 8.314 J/mol*K, we get a pressure of 159,568 Pa. This is the force exerted on each side of the box at 24.0 C.

To calculate the force at 108 C, we repeat the same steps but with a new temperature of 381.15 K. Plugging in the same values, we get a pressure of 706,240 Pa. This is the force exerted on each side of the box at 108 C.

It is important to note that as the temperature increases, the force exerted by the gas also increases. This is because as the temperature increases, the gas molecules have more energy and therefore collide with the walls of the box with greater force. This can also be seen in the ideal gas law, where pressure is directly proportional to temperature.