- #1

chocopanda

- 15

- 1

- Homework Statement
- I'm translating my exercise to English so please bear with me.

We are mixing air (an ideal gas) with Volume V1 = 3,00m^3 and Temperature T1 = 150,0C with additional air V2 = 8,00m^3 and T_2 = 5,0C. What is the final temperature and total volume if the pressure p remains constant throughout?

- Relevant Equations
- We learned that for a gas with constant pressure, the following applies: V/V0 = T/T0

To be honest, thermodynamics is really not my strong suit and I get confused when and how to apply formulas. My thought process is as follows:

- there are two ideal gases (ideal gas law applies)

- the pressure remains constant (isobaric process), so p

- I imagine there being two adjacent boxes separated by a wall: 1 box is filled with V1, T1 and the other one is filled with V2, T2. To start the mixing process, we get rid of the "connecting wall" and the two gases begin to mix until an equilibrium sets in. Since the two gases have different temperatures, the final temperature at the end is lower than T1. since V2 is much, much colder than V1 and has almost thrice the volume.

I don't think we can simply sum up both volumes and then calculate the temperature, since a volume shrinks when its temperature drops. I think I would try calculating the final temperature first, then with it the volume, but I get so confused since every formula kinda needs both V and T.

For example for the final volume, I could apply something like V = (V_1 + V_2) * T where T is the final calculated temperature, but my confidence on how to apply laws kinda shattered last week since I bombed the mandatory practice exercises (I got around 20% of the points :( I was so sure I got them right...)

I will be forever grateful for any help. If it helps, we are in our 4th week of theromdynamics lectures, so we haven't had stuff like enthalpy, specific heat capacity, heat Q,...

- there are two ideal gases (ideal gas law applies)

- the pressure remains constant (isobaric process), so p

_{1}= p_{2}= p- I imagine there being two adjacent boxes separated by a wall: 1 box is filled with V1, T1 and the other one is filled with V2, T2. To start the mixing process, we get rid of the "connecting wall" and the two gases begin to mix until an equilibrium sets in. Since the two gases have different temperatures, the final temperature at the end is lower than T1. since V2 is much, much colder than V1 and has almost thrice the volume.

I don't think we can simply sum up both volumes and then calculate the temperature, since a volume shrinks when its temperature drops. I think I would try calculating the final temperature first, then with it the volume, but I get so confused since every formula kinda needs both V and T.

For example for the final volume, I could apply something like V = (V_1 + V_2) * T where T is the final calculated temperature, but my confidence on how to apply laws kinda shattered last week since I bombed the mandatory practice exercises (I got around 20% of the points :( I was so sure I got them right...)

I will be forever grateful for any help. If it helps, we are in our 4th week of theromdynamics lectures, so we haven't had stuff like enthalpy, specific heat capacity, heat Q,...