Calculate the work done in an external combustion engine

[curiouschris]

Hi

Not a homework question, just a fool tinkering...

I have been messing around with the concepts of a stirling engine, and have been looking at other engines which do not use an explosive mixture (petrol etc) as their heat source.

I have to say I am having trouble getting my head around doing what I thought would be a simple calculation.

When calculating the pressure of 1 litre of air(dry air) at 20c I get the following..

P=(nRT)/V
n R T V P?
28.97 8.314 293.15 1 70607.10643 (70.6kPa)

Does this mean 28.97 moles of dry air in a 1 litre container at 20c will have an internal pressure of 70.6kPa? or have I got that all wrong?


What I wanted to work out was a way to calculate the pressure on a piston using different gasses in the following configuration...

Assuming a cylinder with a piston at one end and closed at the other, no leaks around the piston (uses acme no leak rings)

An initial volume of 0.25 litres
A final volume of 1.0 litre
Initial pressure in the cylinder of 101kPa at 25c (standard temp and pressure?)

Given the temperature of the gas within the cylinder was raised to 50c instantly.

Using plain dry air as an example how would I calculate the pressure exerted on the piston?
I realize I have to subtract 101kPa from the result to get the actual working pressure at sea level.

How would I calculate the initial pressure (piston fully 'home') ?
How would I calculate the final pressure (piston fully extended) ? (I assume I would divide the previous result by 4)


When using different gasses and gas mixes do I simply replace the molar value with the value or sum of values of the new gas mixture?

Ta in advance
CC

 

[Andrew Mason]

Hi

Not a homework question, just a fool tinkering...

I have been messing around with the concepts of a stirling engine, and have been looking at other engines which do not use an explosive mixture (petrol etc) as their heat source.

I have to say I am having trouble getting my head around doing what I thought would be a simple calculation.

When calculating the pressure of 1 litre of air(dry air) at 20c I get the following..

P=(nRT)/V
n R T V P?
28.97 8.314 293.15 1 70607.10643 (70.6kPa)

Does this mean 28.97 moles of dry air in a 1 litre container at 20c will have an internal pressure of 70.6kPa? or have I got that all wrong?

one mole of any gas will occupy 22.4 litres at STP: 0 C and one atmosphere pressure. You are making two errors: n has units of moles, not grams. V has units of m^3 not litres.

You can figure this out from PV=nRT: P = 101,325 Pa; n=1; R = 8.3145;T=273

AM

 

[curiouschris]

Thanks Andrew

I have found a tutorial on khan academy that is helping. I'll retry my question once I have a better grasp on it.

I had a longer answer but I was logged out and lost it :(

 

[Andrew Mason]

What I wanted to work out was a way to calculate the pressure on a piston using different gasses in the following configuration...

Assuming a cylinder with a piston at one end and closed at the other, no leaks around the piston (uses acme no leak rings)

An initial volume of 0.25 litres
A final volume of 1.0 litre
Initial pressure in the cylinder of 101kPa at 25c (standard temp and pressure?)

Given the temperature of the gas within the cylinder was raised to 50c instantly.

Using plain dry air as an example how would I calculate the pressure exerted on the piston?
I realize I have to subtract 101kPa from the result to get the actual working pressure at sea level.

How would I calculate the initial pressure (piston fully 'home') ?
How would I calculate the final pressure (piston fully extended) ? (I assume I would divide the previous result by 4)

So you start with a cylinder of air at 101 kPa pressure and 25C temperature with a piston that confines the air to .25 litre. You then heat the gas to 50C instantly and the air then expands to 1 litre.

First you want to know the initial pressure in the cylinder after the air temperature is raised to 50C. To do this just use the ideal gas law: P/T = constant (T in Kelvin) where V is constant.

Second, you want to know the final pressure in the cylinder after expansion. This is an adiabatic expansion from air at an initial temperature of 50C. To calculate that, we would need to know the external pressure on the piston. The reason for this has to do with the first law of thermodynamics. We have to determine how much work was done in expansion. That energy comes out of the internal energy of the gas. ie since this is an adiabatic expansion, Q = 0 so ΔU = -W where W is the work done BY the gas.

AM