Confusion regarding Thermodynamics - Molar Specific Heats for Gases

In summary, the problem involves determining the heat added to a 2.00 mole sample of nitrogen gas at 0 degrees C that is heated to 150 degrees C at constant pressure. The relevant equations for this problem include Q = nCpΔT, Q = (change in internal energy) + PΔV, and (internal energy) = (5/2)nRT for a diatomic gas. However, the first equation does not work and it is unclear why. The correct equation to use is Q = n(7/2)RT due to Cp = CV + R. The solution is eventually found, but the issue with the first equation remains unresolved.
  • #1
HolyArrow
2
0

Homework Statement


From Giancoli's UC Berkeley edition Physics for Engineers and Scientists:
A 2.00 mole sample of N2 (nitrogen) gas at 0 degrees C is heating to 150 degrees C at constant pressure (1.00 atm). Determine the heat added to it.

Homework Equations


Variables in equations: V = volume, P = pressure, C = Molar Specific Heat, n = moles, T = temperature, Q = heat

(I thought this was relevant but apparently it isn't and I don't understand why): Q = nC(delta T), with C being the molar specific heat constant for Nitrogen at constant pressure.

(actually relevant): for a process at constant pressure, Q = (change in internal energy) + P(delta V), which I can see is just the first law of thermodynamics.

Also, (internal energy) = (5/2)nRT for a diatomic gas

The Attempt at a Solution


This is kind of a request for clarification, rather than at solving the actual problem. Basically, right when I read the problem, I thought to myself that the first equation above (Q = nC(delta T)) would be the solution. It explicitly states in the book that the heat Q needed to raise the temperature of n moles of gas by delta T is given by that equation. However, that equation doesn't work. I eventually figured out that I'd have to use some equations on the next page, which are the other relevant equations that I posted, to solve the problem. So, I was able to get the solution. However, I still don't understand why the first equation I tried failed to work, and that bothers me. I am certain that I used the correct SI units. Any help?
 
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  • #2
The equation Q = nCpΔT should work for a constant pressure process unless you used an incorrect value for Cp. In your "attempt for a solution" you don't specify what you used for C. You should have used Cp. Don't forget that Cp=CV+R which in this case gives Cp=(7/2)R.
 
  • #3
I apologize for the lack of clarity. I indeed used the correct CP, so I really don't know what I did wrong. It's pretty infuriating. I checked back and forth countless times to make sure I didn't misread; the process is indeed one of constant pressure.
 
  • #4
So you did

Q=n*7/2*R*150K

because using first law gives the same equation

Q=5/2nR*∆T+nR∆T=7/2nR∆T
 
  • #5


First of all, it is important to note that the equation Q = nC(delta T) is only valid for an ideal gas undergoing a constant volume process. In this problem, the gas is undergoing a constant pressure process, so this equation cannot be used.

As you have correctly stated, for a process at constant pressure, the heat added (Q) is equal to the change in internal energy plus the work done by the gas. In this case, since the volume is constant, the work done by the gas is zero. Therefore, the equation becomes Q = (change in internal energy).

The reason why the equation Q = nC(delta T) did not work is because it does not take into account the change in internal energy. It only considers the change in temperature, which is not enough information to calculate the heat added for a constant pressure process.

In order to solve this problem, you would need to use the equation Q = (change in internal energy), which can be calculated using the equation (internal energy) = (5/2)nRT for a diatomic gas.

I hope this helps clarify the confusion regarding thermodynamics and molar specific heats for gases. It is important to carefully consider the conditions of the problem and use the appropriate equations to solve it.
 

1. What is the difference between molar specific heat and specific heat?

Molar specific heat is the amount of heat required to raise the temperature of one mole of a substance by one degree, while specific heat is the amount of heat required to raise the temperature of one unit mass of a substance by one degree.

2. Why do gases have two different molar specific heats?

This is due to the fact that gases have two types of molecular motion: translational motion (movement of the entire molecule) and rotational motion (movement of the molecule around its center of mass). Therefore, two different values are needed to account for the energy required for each type of motion.

3. How do molar specific heats vary with temperature for gases?

For ideal gases, molar specific heats remain constant at all temperatures. However, for real gases, molar specific heats can vary slightly with temperature, but the change is usually negligible for most practical purposes.

4. How do molar specific heats differ for different gases?

The molar specific heats for gases depend on the molecular structure and composition of the gas. For example, diatomic gases like oxygen and nitrogen have different molar specific heats compared to monatomic gases like helium and argon.

5. How are molar specific heats measured for gases?

Molar specific heats for gases can be measured experimentally using a calorimeter. The gas is placed in a container and heated, and the change in temperature is measured. The heat capacity of the container is also measured, and from these values, the molar specific heat of the gas can be calculated.

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