# PV Diagram help - Monatomic ideal gas change of state

• prj
In summary, the conversation discusses the calculation of total work, change in internal energy, and heat flow for a monatomic ideal gas undergoing a process from state A to state D shown on a PV diagram. The total work done on the gas is found to be 1215.6 J if it follows a constant volume path A-B and then a constant pressure path B-C-D. To determine the change in internal energy, the ideal gas law can be used to write it in terms of pressure and volume rather than the number of moles and temperature.
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.

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?

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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?

prj said:
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.

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

Thank you for the help!

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.

## 1. What is a PV diagram and how is it used?

A PV diagram, also known as a pressure-volume diagram, is a graphical representation of the changes in pressure and volume of a system as it undergoes a change of state. It is used to visualize and analyze the thermodynamic processes of a system, such as expansion and compression, and can provide information about the work done on or by the system.

## 2. What is a monatomic ideal gas?

A monatomic ideal gas is a theoretical gas that consists of single atoms that do not interact with each other and follow the ideal gas law, which states that the pressure, volume, and temperature of a gas are directly proportional to each other. Real gases may behave similarly to an ideal gas under certain conditions, but they do not always follow this law.

## 3. How is the change of state of a monatomic ideal gas represented on a PV diagram?

The change of state of a monatomic ideal gas is represented by a curve on a PV diagram. When the gas is heated or compressed, the curve will shift upwards and to the left, indicating an increase in pressure and decrease in volume. When the gas is cooled or expanded, the curve will shift downwards and to the right, indicating a decrease in pressure and increase in volume.

## 4. What information can be obtained from a PV diagram of a monatomic ideal gas?

A PV diagram can provide information about the work done on or by the system, as well as the efficiency of the process. It can also show the direction and magnitude of the change in pressure and volume, and can be used to calculate other properties of the gas, such as its temperature and internal energy.

## 5. What are some limitations of using a PV diagram for a monatomic ideal gas?

One limitation is that it assumes the gas behaves like an ideal gas, which is not always the case. Additionally, the PV diagram only shows the changes in pressure and volume, and does not provide information about the specific processes or interactions that occur within the gas. It is also limited in its ability to accurately represent the behavior of real gases, which may deviate from the ideal gas law at high pressures or low temperatures.

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