Thermal Physics Problem: Determining Volume & Cp/CV for Ammonia Gas

[10-D King]

1. Determine the volume occupied by a 1 mole of an ideal gas at 27° C and 1 atm pressure. Ammonia gas at 27° C and 1 atm is passed at a rate of 41 cm3 s-1 into an apparatus where it flows over an electrically heated wire of resistance 100 . When the heating current is 50 mA the gas leaves the apparatus at 31.09° C. Calculate Cp and CV for ammonia assuming it behaves as an ideal gas.


3. I know it a pretty simple problem but it has been a while since i practiced any thermal physics. I have determined the initial volume occupied by the ideal gas using:

pV=nRT... and got 0.025m^2

However i am clueless as to how to approach the rest of the problem.

any help would be greatly appreciated.

 

[Redbelly98]

Welcome to Physics Forums.

1. Determine the volume occupied by a 1 mole of an ideal gas at 27° C and 1 atm pressure. Ammonia gas at 27° C and 1 atm is passed at a rate of 41 cm3 s-1 into an apparatus where it flows over an electrically heated wire of resistance 100 . When the heating current is 50 mA the gas leaves the apparatus at 31.09° C. Calculate Cp and CV for ammonia assuming it behaves as an ideal gas.


3. I know it a pretty simple problem but it has been a while since i practiced any thermal physics. I have determined the initial volume occupied by the ideal gas using:

pV=nRT... and got 0.025m^2

However i am clueless as to how to approach the rest of the problem.

any help would be greatly appreciated.

Since you're told the resistance and current of the heater, you can figure out how many Joules are given off by the wire every second. You can also figure out how much gas (at 27 C and 1 atm) passes over the wire every second. Then you'll know that a certain amount of energy heats a certain amount of gas ... hopefully that gets you going on working through the problem.

 

[10-D King]

Okay so i found that you get 0.25J/s of energy and that in one second, 4.1x10⁵m³s^-1

not sure where to go from here. What process is this?

do i need to find γ to find the heat capacities?

 

[Redbelly98]

Okay so i found that you get 0.25J/s of energy and that in one second, 4.1x10⁵m³s^-1

Looks good -- assuming you really meant 4.1x10^-5m³ in the volume expression

So you have an amount of energy added by heating, an amount of gas, and an amount of temperature change ... the required information to find heat capacity.

not sure where to go from here. What process is this?

If I read the problem statement carefully:

Ammonia gas at 27° C and 1 atm is passed at a rate of 41 cm3 s-1 into an apparatus where it flows over an electrically heated wire ...

... it sounds like a constant pressure process.

do i need to find γ to find the heat capacities?

No, not for this problem. After you figure out either Cp or Cv, there is a relation for ideal gases between Cp and Cv that you can use to get the other one.

 

[10-D King]

Ha yeh that's what I meant lol

So i have ΔU from the energy per second, the temperature change,

When you talk about the amount of gas, do i need to use the 4.1x10^-5m³s^-1 and the gas that is actually occupied by one mole to find the number of moles of gas that passes in 1 second.

then use ΔU=nC_vΔT to get the heat capacity?

 

[Redbelly98]

Ha yeh that's what I meant lol

So i have ΔU from the energy per second, the temperature change,

When you talk about the amount of gas, do i need to use the 4.1x10^-5m³s^-1 and the gas that is actually occupied by one mole to find the number of moles of gas that passes in 1 second.

Yes, you would use the number of moles of gas in the 4.1x10^-5m³ volume.

... then use ΔU=nC_vΔT to get the heat capacity?

Is this a constant pressure or constant volume process?

 

[10-D King]

From what you were saying it think its a constant pressure process, so it would be ΔH=nC_pΔT

What is the ideal gas equation to find the other heat capacity?

 

[Redbelly98]

From what you were saying it think its a constant pressure process,

That is my impression from the wording of the problem statement, which states a pressure value for the flowing gas.

so it would be ΔH=nC_pΔT

Yes.

What is the ideal gas equation to find the other heat capacity?

Cp and Cv differ by a constant -- it should be in your textbook.