# Basic Thermodynamics: Gas expansion against a vacuum

## Homework Statement

Okay, so the problem given is that there is a rigid tank with a partition down the middle. For partition A, the specific volume, the temperature, and therefore the pressure is known. The mass, or total volume is not known.
Partition B is a vacuum for which the total volume is known.

Temp A = 300 degrees C
Pressure A = 200 kPa
Specific Volume A = 1.31623 m^3/kg

Volume B = 0.2 m^3

Then the partition is removed, and heat is added to the final system so that it remains at a constant pressure. The gas can be modeled as ideal.

Pv = RT
PV = mRT
du = Cv*dT
dh = Cp*dT

## The Attempt at a Solution

My problem is that I don't see how to find any intensive properties for the final system, because partition A is all in intensive properties, and partition B is defined by extensive properties... I can't think of any approach to this problem. I understand that the work done is zero, because it is an ideal gas expanding against a vacuum. I'm currently trying to understand the process as two parts, a gas expanding into a vacuum doing no work, with temperature constant, and volume increasing while pressure decreases. Then heat is added to increase the pressure back to the original value, increasing the temperature as well. But without knowing the relative sizes of the partitions, or the total mass involved for this process, how can the final temperature of the equilibrated system be found??

## Answers and Replies

Andrew Mason
Homework Helper
First find R for this gas using the pre-expansion data. Then use that value for R in determining the final temperature after expansion.

AM

Can you explain a little bit more?

Since P is known for the final state, and R is known, but neither V, v, or T is known, how would you solve for Temperature in PV = mRT or Pv = RT?

Thank you for the reply.

Andrew Mason
Homework Helper
Can you explain a little bit more?

Since P is known for the final state, and R is known, but neither V, v, or T is known, how would you solve for Temperature in PV = mRT or Pv = RT?
You also know how the original volume is related to the final volume. (hint: the partition is down the middle).

AM

rude man
Homework Helper
Gold Member
If the partition is "down the middle", then volume B IS known, so we have a contradiction in the problem's stating.

Anyway: what exactly are you supposed to determine?