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6.5 · Select ideal-gas or real-gas data without mixing models

Learn to select ideal-gas or real-gas data without mixing models through clear examples and targeted practice.

University of Alberta MEC E 340: Applied Thermodynamics

Gas Mixtures and Real Gases

MEC E 340 Applied Thermodynamics — Study topic 6.5

Begin with the stated system and working fluid. In the examples below, the system is either a closed amount of gas or a steady-flow compressor control volume, and each has two numbered states. The topic is not to decide which model is universally better; it is to select the model supported by the problem’s assumptions and available data, then use that model consistently. No property-table values are assumed unless a problem supplies them.

What you will learn

Identify whether a problem calls for an ideal-gas model or real-gas property data.
Keep equations, property values, and assumptions consistent with the selected model.
Use supplied data to calculate an energy change and check units and physical plausibility.

1. Review: what the model choice changes

The first law relates energy transfer to changes in stored energy. For a steady-flow device, a useful simplified balance per unit mass is heat transfer in minus work transfer out equals the change in enthalpy, when changes in kinetic and potential energy are negligible. This balance does not itself tell you whether to use ideal-gas or real-gas properties; the property model must fit the stated assumptions.

For an ideal gas, pressure, specific volume, and temperature obey the ideal-gas equation, and internal energy and enthalpy depend on temperature alone. If specific heats are treated as constant, energy changes can be calculated from those specific heats and the temperature change. If the problem provides ideal-gas property tables with temperature-dependent values, use those instead of a constant-specific-heat approximation.

For a real gas, use the supplied real-gas property data or a stated real-gas model. Real-gas enthalpy or internal energy may depend on more than temperature. Do not take a real-gas enthalpy from a table and combine it with an ideal-gas enthalpy-change formula unless the problem explicitly establishes that approximation.

Pv=RT

A balance equation and a property model do different jobs: the balance tracks energy; the model supplies properties.
Use the source and assumptions given in the problem, such as an ideal-gas assumption or a named property table.
Keep the same model for all states in one calculation.

2. Choose the model before reading properties

First identify the working fluid, system boundary, and states. For a closed system, track the same fixed mass from state 1 to state 2. For a compressor, define a control volume around the device, with inlet state 1 and outlet state 2. State numbers must match the data and the balance.

Next inspect the problem statement and data source. If the problem says to model the gas as ideal, use ideal-gas relations and ideal-gas tables or stated specific heats. If it supplies real-gas properties, use those properties at the specified states. If it gives a real-gas chart or table, do not silently replace its values with ideal-gas values. If no model is specified and the provided information does not support a clear choice, state what additional information is needed rather than inventing data.

Pressure and temperature can help assess whether an ideal-gas assumption is reasonable, but they are not a substitute for the problem’s stated assumptions or supplied data. In particular, do not invent a phase boundary or assume a gas is ideal merely because the calculation is easier.

For steady operation with one inlet and one outlet and no mass accumulation, the mass-flow rate in equals the mass-flow rate out. With negligible kinetic and potential energy changes, the steady-flow energy balance can be written using inlet and outlet enthalpies. State the chosen sign convention before applying it: here, heat into the control volume and work out of it are positive.

q-w=h_2-h_1

Ideal-gas model: use ideal-gas relations and properties consistently.
Real-gas model: use the supplied real-gas property values consistently.
Do not switch models partway through a calculation without an explicit, justified approximation.

3. Read data and calculate consistently

Check each property’s basis and units before using it. Specific enthalpy may be reported in kilojoules per kilogram, while temperature may be in kelvins or degrees Celsius. Temperature differences have the same numerical size in kelvins and degrees Celsius, but absolute-temperature relations require kelvins. Convert units before substitution.

For an ideal gas with constant specific heat, the enthalpy change is specific heat times the temperature change. Use this only when the gas is treated as ideal and the constant-specific-heat approximation is stated or appropriate to the supplied problem. If ideal-gas tables provide enthalpy values at both temperatures, subtract those values instead.

For a real gas, find the relevant properties at each stated state from the supplied real-gas source, then take the difference required by the balance. The table’s reference level may make individual enthalpy values look unfamiliar; the difference between states is what enters the balance. Do not combine enthalpy values from unrelated sources unless their reference bases are known to match.

After calculating, check the sign and units. For a compressor receiving work with negligible heat transfer, outlet enthalpy should exceed inlet enthalpy when work input is positive. A result with inconsistent units, an unexplained sign reversal, or properties read at the wrong state signals that the model or bookkeeping needs review.

\Delta h=c_p(T_2-T_1)

Match each property to the correct state and source.
Use one property basis and consistent SI units throughout.
Check energy-flow directions against the device and the result.

Worked example

1. Constant-specific-heat ideal-gas calculation

A closed system contains 1.50 kg of nitrogen, treated as an ideal gas with constant specific heat

c_v=0.743\ \mathrm{kJ/(kg\cdot K)}

. Its temperature rises from 300 K to 360 K. Find the change in internal energy. Neglect changes in kinetic and potential energy. The gas model and specific heat are supplied assumptions.

Define the system and model
The system is the fixed 1.50 kg mass of nitrogen, from state 1 at 300 K to state 2 at 360 K. The stated ideal-gas model and constant specific heat permit using the ideal-gas internal-energy relation.
Apply the property relation
For the stated constant- $c_v$ model, the total internal-energy change is mass times specific heat times the temperature rise. The kelvin difference is 60 K.
$\Delta U=mc_v(T_2-T_1)$
Calculate
Substitute the supplied values. The kilogram and temperature units cancel, leaving kilojoules.
$\Delta U=(1.50\ \mathrm{kg})(0.743\ \mathrm{kJ/(kg\cdot K)})(60\ \mathrm{K})=66.9\ \mathrm{kJ}$

Answer: The internal energy increases by 66.9 kJ.

Check: A temperature rise gives a positive internal-energy change under the stated ideal-gas model. The result has units of energy and uses only the supplied ideal-gas specific heat.

Worked example

2. Use supplied real-gas enthalpies for a compressor

A steady-flow compressor handles a gas. The problem directs you to use its supplied real-gas property data. At inlet state 1, the tabulated enthalpy is 410 kJ/kg; at outlet state 2, it is 468 kJ/kg. Assume one inlet and one outlet, negligible heat transfer, and negligible kinetic and potential energy changes. Find the compressor work input per unit mass.

Compressor control volume

Steady-flow gas compressor; state 1 is the inlet and state 2 is the outlet. Heat transfer is negligible and work is input.

Set the control-volume balance
The working fluid is the stated gas, with inlet state 1 and outlet state 2. Use the real-gas enthalpies supplied in the problem. With heat into the control volume positive and work out positive, the steady-flow balance applies under the given negligible-energy-change assumptions.
$q-w=h_2-h_1$
Apply the stated assumptions
Negligible heat transfer gives $q=0$ . The compressor requires work input, so work out is negative. Rearranging gives the positive work-input magnitude. w_{in}=h_2-h_1
Calculate from real-gas data
Subtract the supplied inlet enthalpy from the supplied outlet enthalpy. Do not substitute an ideal-gas specific-heat estimate for this difference. w_{in}=468-410=58\ kJ/kg

Answer: The compressor work input is 58 kJ/kg.

Check: The outlet enthalpy is higher than the inlet enthalpy, consistent with work input to an insulated compressor under the stated assumptions. The calculation uses only the supplied real-gas enthalpies.

Worked example

3. Diagnose a mixed-model calculation

A gas compressor problem supplies real-gas enthalpies

h_1=300\ \mathrm{kJ/kg}

and

h_2=355\ \mathrm{kJ/kg}

, and states that heat transfer and kinetic and potential energy changes are negligible. A proposed solution instead estimates the enthalpy change as

c_p(T_2-T_1)

using an ideal-gas constant specific heat not supplied by the problem. Identify the valid calculation and explain why the proposed one is not justified.

Compressor control volume

Steady-flow gas compressor; state 1 is the inlet and state 2 is the outlet. The supplied real-gas enthalpies are used; heat transfer is negligible.

Choose the supported property model
The stated real-gas enthalpies are the supplied property data. Use their difference in the steady-flow energy balance; do not introduce an unsupplied ideal-gas specific heat.
$h_2-h_1=355-300=55\ \mathrm{kJ/kg}$
Interpret the result for the compressor
With negligible heat transfer, the enthalpy rise is supplied by work input. Therefore the required work input per unit mass is 55 kJ/kg. w_{in}=55\ kJ/kg
Explain the model mismatch
The proposed calculation substitutes an ideal-gas relation and a specific heat that the problem does not provide. It is not supported by the stated real-gas data. An ideal-gas estimate would require an explicit ideal-gas assumption and the needed specific-heat information.

Answer: Use the supplied real-gas enthalpy difference; compressor work input is 55 kJ/kg under the stated assumptions.

Check: The enthalpy rise is positive, and the work direction is into the compressor. The result follows directly from the real-gas data without mixing models.

Common mistakes and how to avoid them

Using a real-gas enthalpy at one state and an ideal-gas specific-heat relation for the change to another state.

Correction: Use one property model across both states, unless the problem explicitly states and supports an approximation.

Assuming that any listed property value is suitable, without checking its source or model.

Correction: Check whether the problem specifies ideal-gas data, real-gas data, or a particular approximation before calculating.

Treating a table’s enthalpy reference level as an energy transfer.

Correction: Use the state-to-state enthalpy difference in the balance, and ensure the values come from a consistent source and basis.

Reporting compressor work as work delivered by the device when the balance uses work out as positive.

Correction: State the sign convention and distinguish work input from work output; a compressor requires work input.

Lesson summary

Identify the working fluid, system or control volume, states, and stated assumptions before selecting properties.
Use ideal-gas relations with ideal-gas data, or use supplied real-gas properties consistently.
For a steady-flow device, apply the energy balance with a clear sign convention and the stated negligible terms.
Check state matching, units, signs, and whether the result agrees with the physical direction of energy transfer.

Check your understanding

Question 1

A problem explicitly specifies an ideal gas and supplies ideal-gas enthalpies at states 1 and 2. Which enthalpy change should you use?

The difference between the supplied ideal-gas enthalpies
A real-gas table value at state 2 minus an ideal-gas value at state 1
A specific-heat estimate using an unsupplied value of specific heat
correctIndex

Show answer and explanation

The difference between the supplied ideal-gas enthalpies

The supplied ideal-gas enthalpies match the stated model and provide the state-to-state change directly.

Question 2

An insulated compressor has supplied real-gas enthalpies with

h_2>h_1

. Under negligible kinetic and potential energy changes, what is the energy interpretation?

Work input per unit mass equals $h_2-h_1$
Work output per unit mass equals $h_2-h_1$
The enthalpy rise must be zero because heat transfer is negligible
correctIndex

Show answer and explanation

Work input per unit mass equals

h_2-h_1

With negligible heat transfer, compressor work input raises the flowing gas enthalpy under the stated assumptions.

Question 3

A problem gives only real-gas enthalpies but no ideal-gas assumption or specific heat. Is an ideal-gas enthalpy-change estimate automatically justified?

Yes, because any gas can be treated as ideal without stated assumptions
No; use the supplied real-gas enthalpy difference or request the information needed for another model
Yes, provided the real-gas enthalpies are converted to kelvins
correctIndex

Show answer and explanation

No; use the supplied real-gas enthalpy difference or request the information needed for another model

A different model requires stated support and the needed data; it should not be introduced silently.

Key terms

Ideal-gas model: A gas-property model in which pressure, specific volume, and temperature follow the ideal-gas equation, with internal energy and enthalpy dependent on temperature alone.
Real-gas property data: Supplied property values or a stated model that accounts for real-gas behavior; use the data consistently at the specified states.
Specific enthalpy: Enthalpy per unit mass, commonly reported in kilojoules per kilogram, used in steady-flow energy balances.
Model consistency: Using assumptions, equations, and property values that all represent the same selected gas model.

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