Basic Thermodynamics: Gas expansion against a vacuum

In summary, the problem involves a rigid tank with a partition down the middle, with partition A having known specific volume, temperature, and pressure, while partition B is a vacuum with known total volume. After removing the partition and adding heat to maintain constant pressure, the task is to determine the final temperature of the system. To solve this, one can first find the gas constant R using the pre-expansion data, and then use it to determine the final temperature after expansion. The relationship between the original and final volumes can also be used to solve for the final temperature.
  • #1
irate_turtles
2
0

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.

Homework Equations


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??
 
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  • #2
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
 
  • #3
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.
 
  • #4
irate_turtles said:
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
 
  • #5
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?
 

Related to Basic Thermodynamics: Gas expansion against a vacuum

1. What is the definition of thermodynamics?

Thermodynamics is the branch of science that deals with the relationships between heat, energy, and work. It studies the behavior of systems in response to changes in temperature, pressure, and volume.

2. What is gas expansion against a vacuum?

Gas expansion against a vacuum is the process in which a gas expands into a vacuum or an area with lower pressure. This occurs because gases naturally move from areas of high pressure to areas of low pressure.

3. What are the laws of thermodynamics?

The three laws of thermodynamics are: 1) The law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted. 2) The law of entropy, which states that the total entropy of a closed system will always increase over time. 3) The law of absolute temperature, which states that as a system approaches absolute zero, its entropy approaches a constant minimum value.

4. How does gas expansion against a vacuum relate to the laws of thermodynamics?

Gas expansion against a vacuum follows the first and second laws of thermodynamics. The first law states that energy cannot be created or destroyed, so the energy of the gas must be conserved during expansion. The second law states that the entropy (or disorder) of a closed system will always increase, so the gas will naturally expand into the low pressure area to increase its entropy.

5. What are some real-world applications of gas expansion against a vacuum?

Gas expansion against a vacuum is used in many everyday devices, such as refrigerators, air conditioners, and heat pumps. In these systems, a gas expands against a vacuum to cool down the surrounding area. It is also used in engines, such as in the expansion of hot gases in a car engine to produce movement. Additionally, vacuum pumps use gas expansion against a vacuum to create a vacuum for various industrial and scientific purposes.

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