Go Back   Physics Help Forum > High School and Pre-University Physics Help > Thermodynamics and Fluid Mechanics

Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum

Like Tree2Likes
  • 1 Post By studiot
  • 1 Post By studiot
Reply
 
LinkBack Thread Tools Display Modes
Old Apr 7th 2017, 10:29 AM   #1
Junior Member
 
Join Date: Apr 2017
Location: London
Posts: 5
Ideal Gas Equation - Problem regarding mass

Hi people, I needed some assistance with this problem I came across that involved the use of the ideal gas equation.

Q. A gas cylinder has a volume of 20 litres (20*10^3 m^3). It contains air at a temperature of 17 degrees Celsius and an excess pressure of 3.0*10^5 Pa above the atmospheric pressure 1.0*10^5 Pa. Calculate the mass of air in the cylinder, given that the density of air at STP is 1.3 kg/m^3.

A. 98*10^-3 kg.

My attempted solution at this was:

PV = nRT

By using the equation above we can work out the number of moles "n". So rearranging to make n the subject of the formula.

n = PV/RT

Therefore n = (4*10^5 N/m^2)(20*10^-3 m^3)/(8.31 J/kg*K)(290 K)

We get n to be 3.32 (correct to 3 s.f.)

Since n is also = m/Mr

Where m is the mass in kg and Mr is the molar mass.

m = n*Mr = (3.32)(0.029) = 0.09628 kg

As you can you can see I failed to arrive at the correct answer, and I am unsure why we have been provided the density of air at STP?

I would appreciate any help, thank you in advance!
skengdo410 is offline   Reply With Quote
Old Apr 7th 2017, 05:21 PM   #2
Senior Member
 
Join Date: Jun 2010
Location: NC
Posts: 336
I think you're right. Don't know why the density was included.

Avoid algebra with this equation.

Using the Gas Equation| THERMO Spoken Here!

Victor Regnault | THERMO Spoken Here!

Good Luck with this... JP
Attached Thumbnails
Ideal Gas Equation - Problem regarding mass-ideal_gas_calc.gif  
THERMO Spoken Here is offline   Reply With Quote
Old Apr 8th 2017, 04:18 AM   #3
Junior Member
 
Join Date: Apr 2017
Location: London
Posts: 5
Oh alright, thank you for responding I appreciate it
skengdo410 is offline   Reply With Quote
Old Apr 8th 2017, 03:42 PM   #4
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 452
I don't think this is right at all.

There are several ways to do this but none involved switching to the molar equation.
Where did the question tell you the molar mass of air?

The density was given because it tells you how much is in a given volume, but at a different temperature and pressure from the one the gas is at.

So you must either correct this density to the new temperature and pressure or reduce the given values to STP.

Then you can use the information to obtain the mass of gas.


P1V1/T1 = P2V2/T2

Since you are given P1, P2, T1 and T2 you can correct 20 litres of gas at 4 atm and 17C to V2 litres of gas at STP and multiply by the given density.in kg/litre
skengdo410 likes this.
studiot is offline   Reply With Quote
Old Apr 9th 2017, 06:05 AM   #5
Junior Member
 
Join Date: Apr 2017
Location: London
Posts: 5
@studiot I don't understand how I can make any use of V2? Also V2 is the volume at which the air at STP is occupying right?
skengdo410 is offline   Reply With Quote
Old Apr 9th 2017, 06:19 AM   #6
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 452
Start
You have V1 = 20 litres of gas in a sealed cylinder at P1, T1. (given)
This is a fixed mass of gas.
(Theoretically) Allow this mass of gas to expand to V2 at STP so it is now at 273K and 1atm.

Calculate V2 for this state.

You are given the density of the gas in this state.

Using the density and your calculated V2 you can calculate the mass.

There are many online calculators using this method as it is a common requirement to reduce or correct to STP.
skengdo410 likes this.
studiot is offline   Reply With Quote
Old Apr 9th 2017, 06:30 AM   #7
Junior Member
 
Join Date: Apr 2017
Location: London
Posts: 5
@studiot Bro, thank you so much for the explanation, I have arrived at the correct answer So this means that PV = nRT can only be applied for fixed masses right? And PV = mrT is to be used when the masses change?
skengdo410 is offline   Reply With Quote
Old Apr 9th 2017, 07:03 AM   #8
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 452
You can apply PV = mRmT if you use the correct 'universal' gas constant, Rm in this case. 'm' is the mass of gas not the number of moles.

In this case it is not the constant that uses moles, but the constant that uses mass in its definition.

Good textbooks will offer R in many different units as we often need to swop.
studiot is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Thermodynamics and Fluid Mechanics

Tags
equation, gas, ideal, mass, problem



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
1D wave equation problem jlee07 Advanced Waves and Sound 2 Jan 30th 2017 02:19 PM
work done in an ideal gas problem keanu Advanced Thermodynamics 0 Apr 24th 2016 03:37 PM
Ideal Gas Problem rjsci13 Kinematics and Dynamics 1 Dec 7th 2009 11:42 AM
Differential equation of spring-mass system attached to one end of seesaw TahirMushtaq Kinematics and Dynamics 0 Aug 31st 2009 03:27 AM
3d poisson's equation problem vganpat Advanced Electricity and Magnetism 0 Jan 18th 2009 05:59 AM


Facebook Twitter Google+ RSS Feed