Thermodynamics - Ideal Gas Law

In summary, the problem involves a cylinder containing 2 moles of an ideal monatomic gas at state A with a volume of 1.0 x 10-2 m3 and a pressure of 4.0 x 105 Pa. The gas is then brought isobarically to state B, with a volume of 2.0 x 10-2 m3. From there, it is brought at constant volume to state C, where its temperature is the same as at state A. The gas is then brought isothermally back to state A. To solve the problem, the Ideal Gas Law (PV = nRT) is used. The pressure at state C can be found by using the ideal gas law
  • #1
science.girl
103
0

Homework Statement



A cylinder contains 2 moles of an ideal monatomic gas that is initially at state A with a volume of 1.0 x 10-2 m3 and a pressure of 4.0 x 105 Pa.
The gas is brought isobarically to state B. where the volume is 2.0 x 10-2 m3.
The gas is then brought at constant volume to state C, where its temperature is the same as at state A. The gas is then brought isothermally back to state A.

a. Determine the pressure of the gas at state C.

b. State whether the net work done by the gas during the complete cycle is positive, negative, or zero. Justify your answer.

c. State whether this device is a refrigerator or a heat engine. Justify your answer.


Homework Equations


PV = nRT


The Attempt at a Solution



Well, I have points A and B on a PV diagram. I need to figure out the pressure of the gas at state C to proceed.

I know I have to apply the Ideal Gas Law, but I'm just not sure how. Any help?
 
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  • #2
science.girl said:
The gas is brought isobarically to state B. where the volume is 2.0 x 10-2 m3.
The gas is then brought at constant volume to state C, where its temperature is the same as at state A. The gas is then brought isothermally back to state A.

The gas was brought at constant volume to state C correct? So if the gas was brought to C at constant volume, that means it didnt change, so it has to have the same volume as it did in step B.
 
  • #3
science.girl said:

Homework Equations


PV = nRT

The Attempt at a Solution



Well, I have points A and B on a PV diagram. I need to figure out the pressure of the gas at state C to proceed.

I know I have to apply the Ideal Gas Law, but I'm just not sure how. Any help?
You have the right equation. What is the temperature at B? (apply ideal gas law). What is the change in temperature in going to C? Apply the ideal gas law again to get the change in pressure from B to C.

AM
 
  • #4
wow, sorry for my useless post. for some reason i read it as your problem being you weren't sure what the volume was at C. Follow Andrews steps.
 
  • #5
Andrew Mason said:
You have the right equation. What is the temperature at B? (apply ideal gas law). What is the change in temperature in going to C? Apply the ideal gas law again to get the change in pressure from B to C.

AM

Thank you for your help, Andrew. :smile:
 

1. What is the Ideal Gas Law?

The Ideal Gas Law is a fundamental equation in thermodynamics that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is typically written as 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.

2. What is an ideal gas?

An ideal gas is a theoretical gas that follows the Ideal Gas Law perfectly under all conditions. This means that it has no intermolecular forces, has particles that are infinitely small and have no volume, and undergo elastic collisions with each other and with the walls of the container.

3. How is the Ideal Gas Law derived?

The Ideal Gas Law is derived from combining three gas laws: Boyle's Law, which states that at a constant temperature, the pressure of a gas is inversely proportional to its volume; Charles's Law, which states that at a constant pressure, the volume of a gas is directly proportional to its temperature; and Avogadro's Law, which states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas.

4. What are the units of the gas constant (R) in the Ideal Gas Law?

The units of the gas constant depend on the units used for pressure, volume, temperature, and the number of moles. However, the most commonly used units are atmospheres (atm) for pressure, liters (L) for volume, Kelvin (K) for temperature, and moles (mol) for the number of moles. In this case, the units of the gas constant would be atm·L/mol·K.

5. Under what conditions does the Ideal Gas Law break down?

The Ideal Gas Law assumes that the gas molecules do not interact with each other and that their volume is negligible compared to the volume of the container. Therefore, it breaks down at very high pressures and low temperatures, where the gas molecules are more likely to interact and take up a significant portion of the container's volume. It also does not apply to real gases, which deviate from ideal behavior at high pressures and low temperatures.

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