Calculating Work Done by Ideal Gas: Qualitative Pressure vs Volume

[kawafis44]

1. Calculate the work done by 1 mole of ideal gas in expanding adiabatically from V_1 to V_2 (volumes). Make a qualitative figure of pressure changes as a function volume changes p=p(V).

I will be very grateful for solving this problem because I spent so much time on it and I still do not know how to do it.
Thank you in advance!

 

[physixguru]

The work done by the gas can then be determined. If the final volume is less than the initial, then work is done on the gas and the work will be negative.

 

[Moetasim]

I understand your frustration with this problem. Calculating work done by an ideal gas can be a complex task, but with some guidance, it can be solved.

First, let's start by understanding the concept of work done by an ideal gas. Work is defined as the force applied to an object multiplied by the distance it moves in the direction of the force. In the case of an ideal gas, work is done when the gas expands or compresses against a constant external pressure.

To calculate the work done by an ideal gas in expanding adiabatically, we can use the formula W = -PΔV, where P is the constant external pressure and ΔV is the change in volume. In this case, we are given the initial and final volumes, V1 and V2, so we can calculate the change in volume as ΔV = V2 - V1.

Next, we need to determine the constant external pressure, P. Since we are dealing with an ideal gas, we can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. Since the process is adiabatic, there is no heat exchange, therefore the temperature remains constant. This allows us to rearrange the ideal gas law to solve for pressure as P = (nRT)/V.

Now, we can substitute this value for pressure into our work formula, W = -(nRT/V)(V2-V1). This will give us the work done by 1 mole of ideal gas in expanding adiabatically from V1 to V2.

To create a qualitative figure of pressure changes as a function of volume, we can plot the calculated values of pressure (P) against the changing volumes (V). As the volume increases, the pressure will decrease, following a hyperbolic relationship. This is because as the gas expands, it takes up more space and the molecules are spread out, resulting in a decrease in pressure.

I hope this explanation helps you understand how to calculate the work done by an ideal gas and create a qualitative figure of pressure changes. Remember to always use the appropriate formulas and units when solving scientific problems. Keep up the good work!