Thermodynamic Anomalies

Anomalies in Thermodynamics

Draft Text Only – Readers’ suggestions and inputs are welcome

Thermodynamics is not an easy subject to master and there are many instances where it defies intuitive judgement. The following examples are offered by way of enlightenment and perhaps education:

  • Steam viscosity: it is intuitive knowledge that liquids become less viscous as they get warmer.  Oil becomes thinner as it is heated and syrup gets runnier.  However the opposite is true for gases like steam.  The higher the temperature of superheated steam, the higher its viscosity becomes.  The following examples are taken from steam tables:
Steam Pressure
bar (psi)

Steam Temperature
deg C

Steam Viscosity

17.5 (250) 205 (saturated) 15.9
17.5 (250) 300 20.1
17.5 (250) 400 24.4

The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature. This is due to the increase in the frequency of intermolecular collisions at higher temperatures (reference:

  • Enthalpy reduces with increasing pressure:  A more challenging and less easily explained anomaly is the fact that at constant temperature, the enthalpy and internal energy of steam falls with increase in pressure.

In his book “Hush-Hush: The Story of the LNER 10000“, William Brown quotes from an unidenfied report written circa 1930 that seemed to question the wisdom of high pressure steam in such locomotives as Balwin’s high pressure compound No 60000 and Gresley’s high pressure compound No 10000 of 1929.  The report stated that: “if the (steam) pressure is increased while the temperature remains constant, the superheat and heat content per pound of steam fall off as the pressure is increased. If steam of 200 psi and of 350 psi is expanded from the same temperature under such conditions that the exhaust steam escapes at the same pressure and temperature and with the same heat content in both cases, it follows that the heat taken from the steam in the cylinders and converted into mechanical work will be slightly less with the high than with the low pressure steam. That is, with the same heat content in the exhaust steam, the higher pressure will not give greater thermal efficiency.”

The following examples taken from steam tables illustrate the point:

Steam Temperaure
deg C

Steam Pressure
bar (psi)

Internal Energy

300 13.8 (200) 2786 3041
300 24.1 (350) 2764 3012

Wardale‘s explanation of this phenomenon is instructive (quoted below):

The premise is that steam expanded from high pressure will produce less work than that expanded from a lower pressure and the same temperature if both exhaust at the same pressure and temperature. This would be true, but if comparing like-for-like, which is essential for the given conclusion to be made, the mistake arises because they will not exhaust at the same temperature, and the exhaust steam will therefore not have the same heat content in both cases. This is demonstrated in the following table, taking your own figures for temperature and pressure. (Note two things: steam properties are always given for absolute pressure, not gauge pressure, essentially because steam can (and should, wherever possible, i.e. power station turbines) be expanded to below atmospheric pressure (but don’t even think of it for a locomotive, please), and it is enthalpy we must use as the measure of steam thermal energy, not internal energy because as soon as a piston moves flow work is involved (consult a thermodynamics text book).)

From the enthalpy – entropy chart (Porta’s ‘Mollier diagram’) we have as follows:

Inlet Pressure, psi gauge

200 deg C

300 deg C
Inlet pressure, bar abs. 14.81 25.15
Inlet temperature, deg C 400 400
Inlet steam enthalpy, kJ/kg 3256 3239
Inlet steam entropy, kJ/kg.deg C 7.277 7.014
Exhaust pressure, psi gauge 10 10
Exhaust pressure, bar abs. 1.7 1.7
For an isentropic = constant entropy or ideal expansion in both cases:
Exhaust steam entropy,kJ/kg.deg C 7.277 7.014
Exhaust steam enthalpy, kJ/kg 2731 2633
Heat drop = work done, kJ/kg (3256 – 2731) = 525 (3239 -2633)= 606
Increase in work done for
expansion from higher pressure:
((606 – 525) ÷ 525) x 100% = 15.4%

If the same isentropic efficiency (say 85%) is applied to both cases to give a practical expansion allowing for incomplete expansion loss, etc., the relative values always stay the same.

This gives the correct situation and shows the book’s premise to be wrong because it is based on the false assumption of identical exhaust steam condition for both expansions. However the actual conditions are subject to various factors, making a generalized statement rather meaningless, amongst them:

    1. The above isentropic expansion from 200 psi gauge to 10 psi gauge gives an exhaust steam temperature of about 131°C, which is still superheated. However the corresponding expansion from 350 psi gauge gives saturated steam at 116 °C and dryness fraction 0.972, hence condensation losses at the end of this expansion would be high. But the entropy rise associated with imperfect expansion acts to increase the exhaust steam temperature for all expansions and hence reduce any tendency for condensation.
    2. It is unrealistic to have both expansions start from the same temperature. As the saturation temperature of steam at 350 psi gauge is about 30oC higher than that at 200 psi gauge, if both were superheated to the same temperature the degree of superheat (i.e. the amount by which the superheat temperature is in excess of the saturated temperature) would be that much lower for the former. Rather, as steam at higher pressure would enter the superheater at higher temperature, so the inlet steam temperature at the cylinders would be somewhat higher. This would decrease the tendency for condensation at the end of the expansion.
    3. Simply comparing ultra high with normal inlet pressure without specifying the nature of the engine (i.e. simple or compound) is misleading, compound being more suited to the former, simple to the latter. In the case of a compound, the superheat temperature must be set higher as the greater expansion possible in a compound (giving a higher isentropic efficiency, a fundamental reason for compounding) would otherwise result in saturated exhaust steam.