Calculate the amount of heat supplied to a gas

[MisterP]

Homework Statement

1kmol of multatomy(I hope you understand - gas with many atoms) gas is heated for 100K (conditions of free expansion). I have to calculate the amount of heat supplied to gas. I have no idea how to do it. The right answer is 3320kJ

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

What is your definition of free expansion conditions?

 

[MisterP]

What is your definition of free expansion conditions?

I do not have any definition. It is said in the task. I guess it means, there is nothing influencing the expansion of gas.

 

[Chestermiller]

I do not have any definition. It is said in the task. I guess it means, there is nothing influencing the expansion of gas.

Usually, free expansion is defined as expansion into a vacuum. However, I don't think that is what was intended here. I think what was intended here is expansion against a constant pressure equal to the initial pressure of the gas. If that were the case, then the amount of heat supplied would be equal to the change in enthalpy of the gas. This is given by $$Q=\Delta H=nC_p\Delta T$$where n is the number of moles and $C_p$ is the molar heat capacity of the gas. Are you given no information about the gas? If not, from the answer they gave, what is the molar heat capacity of the gas?

 

[MisterP]

If not, from the answer they gave, what is the molar heat capacity of the gas?

There is nothing more.. Just the temperature - 100K (how much it was risen) and 1kmole, that`s it.. Maybe the fact that it is multi-atom gas changes something?

 

[Chestermiller]

There is nothing more.. Just the temperature - 100K (how much it was risen) and 1kmole, that`s it.. Maybe the fact that it is multi-atom gas changes something?

Not really. What do you calculate for Cp? That might tell us something.

 

[MisterP]

I really do not know.. :(
Edit: or c = Q / (mΔT). ??
But that won`t help..

 

[Chestermiller]

I really do not know.. :(
Edit: or c = Q / (mΔT). ??
But that won`t help..

Let's see the number you get using their answer.

 

[MisterP]

I do not get it. I have not been solving these types of tasks since I was in high school, that's around 13 years ago and now they through all the themes on basic physics and I have to solve this "easily" they say ..

 

[Chestermiller]

I do not get it. I have not been solving these types of tasks since I was in high school, that's around 13 years ago and now they through all the themes on basic physics and I have to solve this "easily" they say ..

Dues the equation I wrote make sense to you? What course is this for?

 

[MisterP]

We had 3 day course on physics - starting mechanics, energy, oscilations, molecular physics, thermodynamics, electrics. I am studying electric engeneering and so, there is this fast course on physics, just for a check. I do understand Your formula, but I do not have Cp.

 

[Chestermiller]

We had 3 day course on physics - starting mechanics, energy, oscilations, molecular physics, thermodynamics, electrics. I am studying electric engeneering and so, there is this fast course on physics, just for a check. I do understand Your formula, but I do not have Cp.

We are trying to "back out" the value of Cp from the answer they gave to see if we can make any sense out of it.

 

[MisterP]

So, I found this. E = x*n*R*T
If x = 4, then I get right answer, but I do not know if this is right. But I have seen that x is 3.
n - moles
R - 8.3 constant
T - temperature

Edit: x = i/2+1
i = 6 for multi atomic gases, so that is how to get 4 and seems like this formula works :)

 

[Chestermiller]

So, I found this. E = x*n*R*T
If x = 4, then I get right answer, but I do not know if this is right. But I have seen that x is 3.
n - moles
R - 8.3 constant
T - temperature

Edit: x = i/2+1
i = 6 for multi atomic gases, so that is how to get 4 and seems like this formula works :)

Very nice.

This is pretty much where I was trying to get you to head (although you didn't appear to want to participate), except the equation should be the same as in my post #2 with $C_p=xR$.

For oxygen and nitrogen, x = 3.5 and i=5, and for carbon dioxide, x = 4.4 and i is about equal to 7. So I guess, in your source, they assign generic values of x = 4 and i = 6 to what they call a generic polyatomic gas.