Calculating Moles and Net Heat in an Ideal Gas Cycle

In summary, the conversation discusses a problem with an ideal gas and a cyclic process. The first part of the question involves finding the number of moles in the sample, while the second part asks for the net heat added to the gas during the cycle. The conversation also mentions the First Law of Thermodynamics and the concept of work done by a system. It ends with a reminder to be mindful of units and a suggestion to find the net heat as the area bounded by the lines on a graph.
  • #1
[rit]panfist
1
0
Hey, my textbook is not helping at all. Here's the problem followed by what I've done on it so far.

A sample of an ideal gas is taken through the cyclic process abca shown in Fig. 20-20; at point a, T = 241 K.

graph:
http://www.webassign.net/hrw/20_20.gif

There are two parts of the question I could not answer. One is how many moles are in the sample? I plugged the values given into pV = nRT, and I got n = .001248. That answer is incorrect.

Secondly, what is the net heat added to the gas during this cycle? I don't know where to begin for this. The textbook is usually very clear, but for some reason doesn't include anything on this.

If anyone could help me get on the right track, I would greatly appreciate it.
 
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  • #2
Do you know the First Law of Thermodynamics?

(Heat Added to a system) = (Change in Internal Energy of system) + (Work done by system on surroundings)

[tex]dQ = dU + dW[/tex]

Also do you know that at constant volume, dW = 0?

Do you think pV = nRT is valid when V is changing?

Cheers
vivek
 
  • #3
You should mind your unit. Beware of the pressure which is in [tex]KN/m_2[/tex] and not [tex]N/m_2[/tex]
 
  • #4
Net heat would be the area bounded by all the 3 lines which is in short the area of the triangle.
 

1. What is the Ideal Gas Law and how does it work?

The Ideal Gas Law is a mathematical equation that describes the behavior of ideal gases, which are gases that follow certain assumptions such as having particles with no volume and no intermolecular forces. The equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This equation shows the relationship between these variables and allows us to calculate any one of them if we know the values of the others.

2. How do I solve an Ideal Gas problem?

To solve an Ideal Gas problem, you will need to use the Ideal Gas Law equation. First, make sure to convert all units to the appropriate SI units (P in Pa, V in m^3, n in moles, T in K). Then, plug in the values you have for three of the variables and solve for the fourth variable. If one of the variables is not given, you can use algebra to rearrange the equation to solve for it. Make sure to pay attention to units and use the correct gas constant for the gas you are dealing with.

3. What are the assumptions of the Ideal Gas Law?

The Ideal Gas Law assumes that the gas particles have no volume, meaning they take up no space themselves. It also assumes that there are no intermolecular forces between the particles, and that the collisions between the particles are perfectly elastic. Additionally, it assumes that the particles are in constant, random motion and that the volume of the container is much larger than the volume of the gas particles.

4. Can the Ideal Gas Law be used for all gases?

No, the Ideal Gas Law can only be used for ideal gases, which are gases that follow the assumptions mentioned above. Real gases do not follow all of these assumptions, especially at high pressures and low temperatures. However, at standard temperature and pressure conditions, most gases behave closely enough to ideal gases that the Ideal Gas Law can be used to make accurate calculations.

5. How does changing the temperature or pressure affect the volume of an ideal gas?

According to the Ideal Gas Law, as the temperature of an ideal gas increases, the volume of the gas will also increase, assuming pressure and number of moles remain constant. This is known as Charles's Law. Similarly, if the pressure of an ideal gas increases, the volume will decrease, assuming temperature and number of moles remain constant. This is known as Boyle's Law.

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