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

 

[sardar]

Hi there,

I would approach this question by first clarifying the terms used. In an external combustion engine, work is done when heat is supplied to the system and is converted into mechanical energy. This work can be calculated by using the formula W = F x d, where F is the force applied and d is the distance traveled. In the case of an engine, this would be the force of the expanding gas pushing on the piston and the distance it travels.

To calculate the work done in an external combustion engine, you would need to know the initial and final volumes of the cylinder, as well as the change in temperature and pressure. The pressure can be calculated using the ideal gas law, as you have shown in your example. However, it is important to note that this formula assumes ideal gas behavior, which may not always be the case in real systems.

To calculate the initial and final pressures, you would need to use the ideal gas law with the initial and final volumes and temperatures. The force on the piston can then be calculated by multiplying the pressure by the surface area of the piston. The distance traveled by the piston can be determined by knowing the change in volume and the geometry of the system.

When using different gases or gas mixtures, you would need to use the appropriate molar value or sum of values in the ideal gas law equation. However, as mentioned before, this may not always accurately reflect the behavior of real gases.

I hope this helps clarify the process of calculating work in an external combustion engine. Keep tinkering and exploring new concepts – that's what science is all about!