SI Units and Core Thermodynamic Quantities in Steam Engineering

Steam engineering calculations depend on a consistent system of units. Pressure, temperature, energy, power, density, specific volume and enthalpy are closely related, and an incorrect unit or pressure reference can change the meaning of an otherwise correct calculation.

The International System of Units, SI, provides a common basis for expressing mechanical and thermal properties. In steam engineering, the most frequently used base quantities include length, mass, time and temperature, together with derived quantities such as force, energy, pressure and power.

Base and derived SI units

• length in metres, m,
• mass in kilograms, kg,
• time in seconds, s,
• temperature in kelvin, K.

The word “specific” generally means that the property is expressed per unit mass.

Temperature: Celsius and kelvin

Temperature indicates the thermal state of a system. Two systems in thermal contact that have the same temperature are in thermal equilibrium.

The Celsius scale is the most familiar scale in engineering practice. The Kelvin scale has the same size increment, but its zero corresponds to absolute zero.

T(K) = T(°C) + 273.15

• 0°C corresponds to 273.15 K,
• 100°C corresponds to 373.15 K,
• absolute zero is 0 K, or -273.15°C.

A temperature difference of 1°C is numerically equal to a temperature difference of 1 K. Temperature differences may therefore be expressed in either scale, while calculations requiring absolute temperature must use kelvin.

Pressure: Pa, bar and pressure reference

The SI unit of pressure is the pascal:

1 Pa = 1 N/m²

Steam systems also commonly use bar:

1 bar = 10⁵ N/m² = 100 kPa

Absolute pressure

Absolute pressure is measured from a perfect vacuum. Therefore, perfect vacuum = 0 bar(a).

Gauge pressure

Gauge pressure is measured relative to atmospheric pressure. A commonly used average atmospheric value at sea level is approximately 1.01325 bar(a).

Gauge pressure = Absolute pressure - Atmospheric pressure

For approximate engineering work:

bar(a) ≈ bar(g) + 1

Differential pressure

Δp = p₁ - p₂

If both pressures use the same reference datum, the numerical differential is the same whether both values are stated as absolute or gauge pressures.

Differential pressure is an important operating quantity in equipment such as pressure reducing valves, control valves and steam traps.

If a valve has an upstream pressure of 8 bar(a) and a downstream pressure of 5 bar(g), the downstream value is approximately 6 bar(a), giving a pressure differential of about 2 bar.

Density, specific volume and relative density

ρ = m / V

v = V / m

v = 1 / ρ

Relative density is a ratio between two densities and therefore has no units. The density of water at the reference condition is approximately 1,000 kg/m³.

Work, heat, energy and power

The SI unit of work and energy is the joule:

1 J = 1 N·m

Work = Force × Displacement

Work = Applied pressure × Displaced volume

For example, 1 N/m² acting through a displaced volume of 1 m³ corresponds to 1 J.

Energy transferred solely because of a temperature difference is heat. Power is the rate of energy transfer:

1 W = 1 J/s

Specific enthalpy

Specific enthalpy describes the energy of a unit mass of fluid associated with its internal energy and the pressure-related work term. In steam engineering it is normally expressed in kJ/kg.

Specific heat capacity and sensible heating

Specific heat capacity at constant pressure, cₚ, describes the change in enthalpy associated with a temperature change at constant pressure. The constant-volume heat capacity, cᵥ, relates to the change in internal energy at constant volume.

For solids and liquids:

cₚ ≈ cᵥ

For water over relatively low temperature ranges:

cₚ ≈ 4.19 kJ/(kg·°C)

The heat required for a temperature change is:

Q = m · cₚ · ΔT

Water-heating example

For 2 litres of water heated from 20°C to 70°C, the mass is approximately 2 kg and the temperature rise is 50°C.

Q = 2 × 4.19 × 50 = 419 kJ

Entropy through heating, evaporation and superheating

When entropy is expressed per unit mass, specific entropy is used, with units of kJ/(kg·K).

For the examples below:

Δs = Δh / Taverage

Heating 1 kg of water from 0°C to 100°C

• Specific enthalpy at 0°C: 0 kJ/kg
• Specific enthalpy at 100°C: 419 kJ/kg
• Average absolute temperature: 323 K

Δs = 419 / 323 = 1.297 kJ/(kg·K)

Evaporation at 100°C

• Specific enthalpy of evaporation: 2,258 kJ/kg
• Absolute temperature: 373 K

Δs = 2,258 / 373 = 6.054 kJ/(kg·K)

The total specific entropy change from water at 0°C to saturated steam at 100°C is:

7.351 kJ/(kg·K)

Superheating steam to 150°C

• Specific enthalpy at 100°C: 2,675 kJ/kg
• Specific enthalpy at 150°C: 2,777 kJ/kg
• Enthalpy increase: 102 kJ/kg
• Average absolute temperature: 398 K

Δs = 102 / 398 = 0.256 kJ/(kg·K)

The total change from water at 0°C to superheated steam at 150°C is:

7.607 kJ/(kg·K)

Engineering checks before using the numbers

• confirm whether pressure is absolute, gauge or differential,
• use absolute temperature in K where required,
• distinguish energy in kJ from energy rate in kW,
• distinguish density in kg/m³ from specific volume in m³/kg,
• state the reference conditions for relative density,
• keep units consistent throughout each equation,
• use thermodynamic properties corresponding to the same pressure, temperature and fluid state.

The same discipline applies when pressure and flow data are used to select flow meters or to evaluate regulating equipment in a steam system.

Conclusion

SI units provide the common framework required for consistent steam-engineering calculations. Correct distinction between absolute, gauge and differential pressure, proper use of absolute temperature and a clear understanding of density, specific volume, enthalpy, heat capacity and entropy are essential for interpreting thermodynamic data correctly.

When units and reference conditions are stated explicitly, engineering calculations become easier to verify, compare and reproduce.

Frequently Asked Questions

What is the difference between bar(a) and bar(g)?

bar(a) is absolute pressure referenced to a perfect vacuum. bar(g) is gauge pressure referenced to atmospheric pressure.

How do I convert °C to K?

Use T(K) = T(°C) + 273.15.

Is a temperature difference of 1°C equal to 1 K?

Yes. Celsius and kelvin have the same size increment, so a 1°C temperature difference is numerically equal to 1 K.

What is differential pressure?

It is the difference between two pressures. If both pressures use the same reference datum, the differential has the same value whether the two pressures are absolute or gauge.

What is the relationship between density and specific volume?

Specific volume is the inverse of density: v = 1/ρ.

How is the heat required to warm a liquid calculated?

Use Q = m·cₚ·ΔT when the specific heat capacity can be treated as constant over the temperature range considered.

What does specific enthalpy represent?

It represents the energy state per unit mass of a fluid, including internal energy and the work associated with pressure.