Source: ENGR/PHYS 216 Final Exam Practice Problems
Tags: closed system, open system, extensive property, intensive property, enthalpy, Universal Accounting Equation, UAE, mass balance, casein, drying, ENGR 216, Texas A&M
This section covers the classification of thermodynamic systems, the distinction between extensive and intensive properties, the Universal Accounting Equation (UAE), and a practical mass balance problem involving drying a dairy product. The conceptual true/false questions here are common exam fodder, so precise definitions matter.
Closed system
A system where no mass crosses the boundary. Energy (heat, work) can still transfer in or out, but the material inside stays put. A sealed piston-cylinder assembly is a classic example.
Open system (control volume)
A system where mass can enter and leave through the boundary. A turbine, pump, or heat exchanger with flow in and out are open systems.
Extensive property
A property that depends on the amount of substance present. If you double the mass of the system, the extensive property doubles. Examples: mass, volume, energy, enthalpy, entropy.
Intensive property
A property that does not depend on the amount of substance. Temperature, pressure, density, and specific enthalpy (enthalpy per unit mass) are intensive. Dividing an extensive property by mass gives the corresponding intensive (specific) property.
Enthalpy (H)
An extensive thermodynamic property defined as H = U + PV (internal energy plus pressure times volume). Because it depends on the total amount of material, it scales with system size.
Universal Accounting Equation (UAE)
The general balance equation for any extensive quantity X:
FINAL − INITIAL = INPUT − OUTPUT + GENERATION − CONSUMPTION
This is the 6-term form. For a conserved quantity (like mass or energy), generation and consumption are both zero, so it simplifies to:
FINAL − INITIAL = INPUT − OUTPUT
A closed system, by definition, does not allow mass transfer across its boundary. Only energy can cross. The statement "mass crosses the boundaries of a closed system" is False.
If mass were crossing the boundary, the system would be open, not closed.
Enthalpy is an extensive quantity: True.
Enthalpy H = U + PV. Since internal energy U and volume V are both extensive (they scale with the amount of substance), H is extensive as well. Specific enthalpy h = H/m would be intensive.
The statement claims the simplified UAE for a conserved quantity is: FINAL − INITIAL = GENERATION − CONSUMPTION
This is False. For a conserved quantity, generation = 0 and consumption = 0, so the right side would just be zero. The correct simplified form is:
FINAL − INITIAL = INPUT − OUTPUT
The full UAE is FINAL − INITIAL = IN − OUT + GEN − CON. Setting GEN = CON = 0 leaves IN − OUT, not GEN − CON.
The statement says INPUT and OUTPUT in the 6-term UAE represent intensive quantities. This is False.
The UAE tracks extensive quantities (amounts that flow in and out of the system). Input and output represent actual amounts of the property being transferred, not rates or per-unit-mass values.
This is a practical application of mass balance. The key principle: the dry solids are conserved through the drying process. Only water is removed.
Given:
1000 kg of wet casein at 25% moisture
Dried to 12% moisture
Wet price: $40/100 kg
Drying cost: $5/100 kg of water removed
Step 1 – Find the mass of dry solids:
Dry solids = 1000 × (1 − 0.25) = 750 kg
The 750 kg of dry solids does not change during drying.
Step 2 – Find the mass of dried product:
In the dried product, dry solids make up 88% (since moisture is 12%): Dried mass = 750 / 0.88 = 852 kg
Step 3 – Find water removed:
Water removed = 1000 − 852 = 148 kg
Step 4 – Drying cost:
Cost = $5 × 148 / 100 = $7.4
Step 5 – Selling price for same profit margin:
Original revenue from 1000 kg wet: $40 × 1000/100 = $400 Total cost to recover: $400 + $7.4 = $407.4 This revenue must come from selling 852 kg of dried product: Price per 100 kg = $407.4 / (852/100) = $407.4 / 8.52 = $47.8 per 100 kg
Universal Accounting Equation (6-term form): FINAL − INITIAL = INPUT − OUTPUT + GENERATION − CONSUMPTION
For conserved quantities (mass, energy): FINAL − INITIAL = INPUT − OUTPUT
Mass balance for drying: Dry solids in = Dry solids out (1 − moisture_in) × mass_in = (1 − moisture_out) × mass_out
⚠️ "Closed system" and "isolated system" are different. A closed system blocks mass transfer but allows energy transfer. An isolated system blocks both.
⚠️ The UAE true/false questions hinge on precise wording. Read each term carefully. The simplified form for conserved quantities eliminates generation and consumption, not input and output.
⚠️ In mass balance problems, identify the conserved component (here, dry solids) and track it through the process. The moisture content is what changes.
⚠️ Extensive = depends on system size (mass, volume, enthalpy). Intensive = independent of size (temperature, pressure, density). A quick test: if you split the system in half, does the property halve (extensive) or stay the same (intensive)?
Q: Can energy cross the boundary of a closed system?
A: Yes. A closed system permits energy transfer (heat and work) but not mass transfer.
Q: Is temperature extensive or intensive?
A: Intensive. It does not depend on the amount of substance. Splitting a system in half does not change its temperature.
Q: In the UAE, what happens to the generation and consumption terms for mass?
A: They are both zero, because mass is conserved (it cannot be created or destroyed in ordinary processes). The UAE simplifies to FINAL − INITIAL = IN − OUT.
Q: 500 kg of a product at 30% moisture is dried to 10% moisture. How much dried product is there?
A: Dry solids = 500 × 0.70 = 350 kg. Dried product = 350 / 0.90 = 388.9 kg.
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