Adiabatic expansion of a balloon

Click For Summary

Homework Help Overview

The discussion revolves around the adiabatic expansion of hydrogen sulfide gas (H2S) in a flexible balloon. The problem involves an initial state with specific volume and temperature, followed by an isobaric expansion and an adiabatic process where the temperature returns to its original value. Participants are tasked with determining the final volume after these processes.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the use of the ideal gas law and the first law of thermodynamics, questioning the application of these principles in the context of the problem.
  • Some participants attempt to derive relationships between temperature, volume, and pressure during the expansions, while others express confusion about the equations and constants involved.
  • There are inquiries about the significance of the gamma value and its role in the adiabatic process.

Discussion Status

The discussion is ongoing, with various participants sharing their attempts and seeking clarification on specific equations and concepts. Some guidance has been provided regarding the adiabatic condition and the use of constants, but there is no clear consensus on the correct approach or solution yet.

Contextual Notes

Participants note the importance of understanding the initial conditions and the implications of the adiabatic process, including the return to the original temperature. There is also mention of potential confusion regarding the calculations and the interpretation of the results.

gmarc
Messages
5
Reaction score
0

Homework Statement



A flexible balloon contains 0.375 mol of hydrogen sulfide gas H2S. Initially the balloon of H2S has a volume of 6750 cm^3 and a temperature of 29.0 C. The H2S first expands isobarically until the volume doubles. Then it expands adiabatically until the temperature returns to its initial value. Assume that the H2S may be treated as an ideal gas with C_p = 34.60 J/mol*K and gamma = 4/3.

What is the final volume in meters cubed?
 
Physics news on Phys.org
gmarc said:

Homework Statement



A flexible balloon contains 0.375 mol of hydrogen sulfide gas H2S. Initially the balloon of H2S has a volume of 6750 cm^3 and a temperature of 29.0 C. The H2S first expands isobarically until the volume doubles. Then it expands adiabatically until the temperature returns to its initial value. Assume that the H2S may be treated as an ideal gas with C_p = 34.60 J/mol*K and gamma = 4/3.

What is the final volume in meters cubed?
Show us your thoughts on this first.

This a first Law problem.

Can you draw a PV diagram of this two stage process? What is the Work done by the gas in the first stage? What is the heat flow into the gas in each stage? What is the total change in internal energy of the gas?

If you answer those questions, you will be able to answer the question.

AM
 
as a continuation of this problem, I tried to solve it by using the equation:

v2^(1/3) = [t1*v1^(1/3)]/t2

Found t2 by:
po=pf=t1/v1=t2/2v1
2t1v1/v1=t2
2t1=t2

so... i got v2^(1/3) = {[299*(7050cm3 *10-9 m3)^1/3] / 598}
v2={0.00958}^3
=8.81 * 10-7

The answer machine says wrong. What did I do wrong? Thanks in advance!
 
You've been given a gamma, why do you think this is?

Recheck the ideal gas adiabatic relations. As this is
 
I may have confused you. This does not require application of the first law. Sorry about that.

Determine the temperature after the first expansion (PV=nRT). Then apply the adiabatic condition (PV^{\gamma} = nRTV^{\gamma-1} = K)to determine the volume when T is back to the original T.

AM
 
I'm confused. What have I done wrong with my equation.

By the way, I'm a different person asking the same question. :)

What is K, the original temperature? And how do you get P, through the p0=t1/v1 equation?
 
minidee said:
I'm confused. What have I done wrong with my equation.

By the way, I'm a different person asking the same question. :)

What is K, the original temperature? And how do you get P, through the p0=t1/v1 equation?
K is a constant. The adiabatic condition is PV^{gamma} = constant.

As far as your equation is concerned, I am not sure what you are doing. You haven't provided any explanation. You have to break the question into two parts. The first part is simple. You can easily find T after the isobaric expansion. To find the volume after the adiabatic expansion you apply the adiabatic condition.

AM
 
I found help elsewhere. Your way with the K constant is actually quite unnecessary. It's faster to use just V1 and gamma. Thanks for coming back and trying to help I guess.
 
minidee said:
I found help elsewhere. Your way with the K constant is actually quite unnecessary. It's faster to use just V1 and gamma. Thanks for coming back and trying to help I guess.
You appear to be applying the adiabatic condition but you seem to be unaware of it.

The adiabatic condition is:

[/tex]PV^{\gamma}=K[/tex]

If you substitute P = nRT/V this becomes:

[/tex]nRTV^{\gamma-1} = K[/tex]

This means that [/itex]TV^{\gamma-1}[/itex] does not change, so:

[/tex]T_2V_2^{\gamma-1} = T_3V_3^{\gamma}[/tex]

T1 = 302K
T2 = 604K
[/itex]V2 = 6750 cm^3 = 6.75 x 10^3 (x 10^{-6}) m^3 = 6.75 x 10^{-3} m^3[/itex]
V3 = 13.50 x 10^{-3}m^3

So:

[/tex](604)(1.350 x 10^{-2})^{1/3} = (302)V_3^{1/3}[/tex]

[/tex]V_3^{1/3} = .476 m^3[/tex]

[/tex]V_3 = .78 m^3 = 7.8 x 10^5 cm^3[/tex]

You started out ok but your numbers are wrong. Also the temperature of 29C is 273+29 = 302K.

(Latex seems to be down so I have put a / in front of the tags so you can see them)
AM
 
  • #10
Andrew Mason said:
You appear to be applying the adiabatic condition but you seem to be unaware of it.

The adiabatic condition is:

[/tex]PV^{\gamma}=K[/tex]

If you substitute P = nRT/V this becomes:

[/tex]nRTV^{\gamma-1} = K[/tex]

This means that [/itex]TV^{\gamma-1}[/itex] does not change, so:

[/tex]T_2V_2^{\gamma-1} = T_3V_3^{\gamma}[/tex]

T1 = 302K
T2 = 604K
[/itex]V2 = 6750 cm^3 = 6.75 x 10^3 (x 10^{-6}) m^3 = 6.75 x 10^{-3} m^3[/itex]
V3 = 13.50 x 10^{-3}m^3

So:

[/tex](604)(1.350 x 10^{-2})^{1/3} = (302)V_3^{1/3}[/tex]

[/tex]V_3^{1/3} = .476 m^3[/tex]

[/tex]V_3 = .78 m^3 = 7.8 x 10^5 cm^3[/tex]

You started out ok but your numbers are wrong. Also the temperature of 29C is 273+29 = 302K.

(Latex seems to be down so I have put a / in front of the tags so you can see them)
AM

How can V_3 = .78 m^3
if
V_3^(1/3) = .476 m^3

3sqrt(V_3) = .476 m^3

V_3 = (.476 m^3)^3 = 0.1078 ?

I have trouble finding delta_U

delta_U = nCv delta_T

T = 300 K
n = 0.35 mol
Cv = 25.95 J/mol*K
delta_T = 0 I not sure about this one
The question states
"Then it expands adiabatically until the temperature returns to its initial value"

The balloon double it volume isobarically and then adiabatically until the temperature returns to its initial value

Please help me
 
Last edited:

Similar threads

Solving Flexible Balloon H2S Gas Problem: Q, ΔU, W & V
  • · Replies 5 ·
Replies
5
Views
25K
Finding the pressure of a gas in three identical balloons
  • · Replies 12 ·
Replies
12
Views
2K
Closed cycle of an ideal gas
  • · Replies 3 ·
Replies
3
Views
2K
Isothermal, isobaric and adiabatic
  • · Replies 6 ·
Replies
6
Views
2K
Thermally insulated container with alternating series of walls
  • · Replies 49 ·
2
Replies
49
Views
3K
Adiabatic expansion with temperature-dependent gamma
  • · Replies 1 ·
Replies
1
Views
2K
Ideal Gas Law -- Isobaric Epansion followed by....
  • · Replies 9 ·
Replies
9
Views
2K
Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
How Is Work Calculated for a Gas and Balloon in Isothermal Expansion?
  • · Replies 11 ·
Replies
11
Views
5K
Volume ratio in an adiabatic gas expansion
  • · Replies 9 ·
Replies
9
Views
2K