PV Diagram help - Monatomic ideal gas change of state

[prj]

Homework Statement

Suppose a monatomic ideal gas is changed from state A to state D by one of the processes shown on the PV diagram (attached). a) Find the total work done on the gas if it follows the constant volume path A-B followed by the constant pressure path B-C-D. b)Calculate the total change in internal energy of the gas during the entire process and the total heat flow into the gas.

Homework Equations

W= -P(Vf-Vi)
dU = Q + W
dU = 3/2nRT

The Attempt at a Solution

I found the answer to part A to be 1215.6 J of work were done on the gas. My problem comes in part b. How can I determine the change in internal energy without knowing the number of moles (n) of the gas, or the temperature?

 

[cosmic dust]

Do you really need n to calculate the change in internal energy? Remember that U depends only on temperature, so what is the temperaure difference?

 

[TSny]

dU = 3/2nRT

How can I determine the change in internal energy without knowing the number of moles (n) of the gas, or the temperature?

Shouldn't that be dU = 3/2nRdT? Or ΔU = Δ(3/2nRT)? Maybe you can use the ideal gas law to write this in terms of P and V rather than nRT.

 

[prj]

I think I was over-complicating the problem, but I've solved it now.

Thank you for the help!

 

[Nickie]

To calculate the change in internal energy, you will need to use the ideal gas law, PV=nRT, where n is the number of moles of gas and T is the temperature. Since the gas is monatomic, the internal energy can be calculated using the equation dU = 3/2nRT. However, in order to solve for dU, you will need to know at least two of the variables (n, T, or R).

One approach would be to assume a reasonable value for the temperature, such as room temperature (around 300 K), and then solve for the change in internal energy using the given pressure and volume values at states A and D. This will give you an approximation of the change in internal energy for the entire process.

Alternatively, you could also use the ideal gas law to calculate the number of moles of gas, assuming that the pressure and volume remain constant throughout the process. Then, you can use this value of n to calculate the change in internal energy using dU = 3/2nRT.

As for the total heat flow into the gas, you can use the first law of thermodynamics, dU = Q + W, to solve for Q. Since you have already calculated the work done on the gas in part A, you can substitute this value for W and solve for Q. Keep in mind that Q can be positive or negative, depending on whether heat is flowing into or out of the gas.