Date: 4/08/2015 17:48:10
From: mollwollfumble
ID: 757069
Subject: Thermodynamics question.

Question.

A small box with air in it at a partial vacuum sits in an infinite air-filled box such as the atmosphere. A valve lets air quickly into the small box until the pressure equilibrates, this valve is closed before the temperature equilibrates. What is the final temperature in the box?

Given: small box initial temperature T1 and pressure P1. External atmosphere temperature Te and pressure Pe. The volume of the box is Vb. The final pressure in the box is P2 = Pe. Find the final temperature in the box T2.

Does the answer depend on the volume of the box?

Reply Quote
Date: 4/08/2015 17:56:15
From: Peak Warming Man
ID: 757073
Subject: re: Thermodynamics question.

Well T2 = (P2 x V2 x T1) divided by (P1 x V1)
So yeah it is volume dependent.

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Date: 4/08/2015 18:24:14
From: btm
ID: 757074
Subject: re: Thermodynamics question.

Peak Warming Man said:


Well T2 = (P2 x V2 x T1) divided by (P1 x V1)
So yeah it is volume dependent.

What are V1 and V2? I assume one of them is the volume of the box; what’s the other? If one’s the volume of the box before it’s filled, and the other’s the volume after it’s filled, why would they be different?

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Date: 4/08/2015 18:53:42
From: Spiny Norman
ID: 757083
Subject: re: Thermodynamics question.

btm said:

What are V1 and V2?

German WW2 rockets.

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Date: 4/08/2015 19:01:41
From: Peak Warming Man
ID: 757087
Subject: re: Thermodynamics question.

btm said:


Peak Warming Man said:

Well T2 = (P2 x V2 x T1) divided by (P1 x V1)
So yeah it is volume dependent.

What are V1 and V2? I assume one of them is the volume of the box; what’s the other? If one’s the volume of the box before it’s filled, and the other’s the volume after it’s filled, why would they be different?

I think this is Molls trick question.
The above schoolboy formula is based on the substance being a gas and having a consistent number of moles.

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Date: 5/08/2015 10:22:55
From: mollwollfumble
ID: 757271
Subject: re: Thermodynamics question.

> I think this is Molls trick question.

Not a trick question. Just one that I’m struggling with (the application is to help in calculating the temperature in unpressurised airplane compartments during descent). “V2” in PWM’s formula is “specific volume” which is defined proportional to 1/density. PWM’s formula is fine, except that the volume Vb is constant so external air at a different temperature needs to fill the void between Vb and V2 and the result involves the mixing of air at different temperatures. Or perhaps it can be solved using heat Q rather than temperature, or internal energy U?

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Date: 5/08/2015 11:08:46
From: wookiemeister
ID: 757286
Subject: re: Thermodynamics question.

in practical terms?

most likely the temperature of the gas that has filled the partial vacuum

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