Find the Mass of the Air, and the Work and Heat Transfer

In summary, the problem involves a piston-cylinder assembly containing air that is initially at 2 bar, 300 K, and 2m3. The air undergoes a process where its pressure decreases to 1 bar, following the relationship pv = constant. Assuming ideal gas behavior, the mass of the air can be calculated using the ideal gas law and the molar mass of dry air. The work and heat transfer can be determined using the first law of thermodynamics.
  • #1
Northbysouth
249
2

Homework Statement


A piston-cylinder assembly contains air, initially at 2 bar, 300 K, and a volume of 2m3. The air undergoes a process to a state where it pressure is 1 bar, during which the pressure-volume relationship is pv = constant. Assuming idea gas behavior for the air, determine the mass of the air, in kg and the work and heat transfer, each in kJ


Homework Equations



pv-nrt

W = ∫p dv




The Attempt at a Solution



I found the constant C to be:

pivi = (200,000 Pa)(2m3)

C = 400,000 Pam3


vf = C/pf

Hence vf = 400,000 Pa m3/100,000 Pa

vf = 4m3

W = ∫P dv = ∫24C/v dv

W = 277258.9 kJ

Mass of air:

pv =nrt

n = (200,000 Pa)(2m3)/(8.314 J/K mol)(300K)

n = 160.372 Pa m3mol/J

I'm a little fuzzy on moles and such, but unless I'm much mistaken, I should be able to find the mass of the air by dividing by Avogadro number, right?

After this, I can calculate the heat transfer with Q = mcΔT in which I can find the ΔT with the relationship:

pivi/Ti = pfvf/Tf

Am I making sense?
 
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  • #2
Northbysouth said:

Homework Equations



pv=nrt

W = ∫p dv

The Attempt at a Solution



I found the constant C to be:

pivi = (200,000 Pa)(2m3)

C = 400,000 Pam3
Units of Pressure x volume = Joules

vf = C/pf

Hence vf = 400,000 Pa m3/100,000 Pa

vf = 4m3

W = ∫P dv = ∫24C/v dv
Since PV = nRT and PV = constant what kind of process is this (hint: what happens to T during this process?)?

W = 277258.9 kJ

Mass of air:

pv =nrt

n = (200,000 Pa)(2m3)/(8.314 J/K mol)(300K)

n = 160.372 Pa m3mol/J

I'm a little fuzzy on moles and such, but unless I'm much mistaken, I should be able to find the mass of the air by dividing by Avogadro number, right?
Use the mass of one mole of dry air and multiply by the number of moles you have found (which is correct).

You can look up the molar mass of dry air. Or you can work it out. Dry air consists of mostly nitrogen (78%) and oxygen (21%). There is about 1% argon and traces of other gases. You have to know that the Nitrogen and oxygen gases are diatomic and argon is monatomic. 14x2(.78)+ 16x2(.21) + 40x1(.01) = 29 g/mol

After this, I can calculate the heat transfer with Q = mcΔT in which I can find the ΔT with the relationship:

pivi/Ti = pfvf/Tf

Am I making sense?
You don't need to work out the temperature change. It is easily seen what happens to T from PV = nRT = constant.

What you need to do here is apply the first law:Q = ΔU + W

Given ΔT what can you say about ΔU? So what is Q?

AM
 

1. What is the mass of air?

The mass of air is the total amount of matter present in a given volume of air. It is measured in units of mass such as kilograms or pounds.

2. How is the mass of air calculated?

The mass of air can be calculated by multiplying the density of air (typically measured in kg/m3) by the volume of air. The volume can be measured using a variety of methods, such as using a gas syringe or measuring the dimensions of a container.

3. What is work transfer in relation to air?

Work transfer in relation to air refers to the transfer of energy in the form of work between a system and its surroundings. In the context of air, this could include work done by a fan to move air or work done by air to turn a wind turbine.

4. How is work transfer related to the mass of air?

The work transfer related to the mass of air is dependent on the velocity and pressure of the air. The higher the mass of air, the more potential there is for work transfer as there is more matter present to interact with the surroundings.

5. What is heat transfer and how is it related to air mass?

Heat transfer is the transfer of thermal energy between a system and its surroundings. In the context of air, this could include heat transfer from a hot air balloon to the surrounding air, or heat transfer from the sun to the Earth's atmosphere. The mass of air can affect heat transfer as it determines the amount of matter present to absorb or transfer heat energy.

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