The engine is driven by a
But, the pressure is created from
It is very easy to measure the pressure inside
the engine. Sensors are very quick acting and
can be taken per revolution. Temperature sensors by comparison,
are very slow responders. They are only good for average
So we can measure the pressure
accurately and quickly. And pressure is distributed throughout the
engine very rapidly. Not so with temperature.
use the pressure to calculate the temperature with the pv/T
= nR formula?
for certain moments of the cycle.
In the beta engine,
when the displacer is at top dead centre, all the gas has to be
the bottom of the displacer and above the piston. And
Likewise, there is a moment when the displacer and the
All the air is above the
displacer. .And hot.
Looking at the diagram of the
sinusoidal motion curves of the bottom of the displacer and
top of the piston, we can calculate the gas volumes at
these two moments.
The vertical gap for cold gas at displacer
TDC is 2.4. For the “kiss”, the hot gap is 1.7.
we use a cross-sectional area of 1, then the volumes are in the
ratio, hot to cold of 1.7 :
Now we use the fact
that the engine has a constant amount of gas in it – at all
So, the term nR, the mass of gas is the same whether
the gas is hot and pressurised or
we know the volumes …... phot
= 1. 7 phot
From measurements of a 90mm atmospheric beta, the
pv work diagram shows that2.4
= 1. 7 x 24 / 8
the pressure varies from 24 psi
down to 8 psi (absolute)
the ratio of hot to cold temperature becomes ……. (1.
7 x 24) / (8 x 2.4) = 2.13
can guess as to the temperature of the cold end. The cooling water
does not boil.
It is less than 100C (373Kelvin). It is also
above ambient say 20C (293K)
Lets settle for somewhere in the
middle - 333K
Using the 2.13 factor, the hot end gas
temp could be 333 x 2.13
the point of all this?
We have a measurement method to
estimate the temperature of the hot gas.
We can measure –
and then manage.
We can assess changes to the burner,
or the hot cap finning.