Qwestrum Engineering360 · Mechanical Engineering · Thermodynamics
First Law of Thermodynamics
(differential form, P.K. Nag sign convention)
Exam tip: lock the sign convention (Q into system, W by system in P.K. Nag) before substituting; use absolute temperature for ideal-gas and efficiency ratios.
Key formulas & points
Skim these first — then read the full notes below.
- State function: U — path independent
- Work W: +ve when done BY system
- Heat Q: +ve when added TO system
Topic details
Introduction
First Law of Thermodynamics is a standard unit in Thermodynamics across Indian B.Tech programmes (RTU, SPPU, Anna University, JNTU, IITs/NITs, and state universities).
Scope in B.Tech and GATE syllabus
You will study this from Engineering Thermodynamics — P.K. Nag. The topic deals with energy, heat, and work in thermal systems and is used in engines, boilers, and refrigeration cycles.
Why this topic matters in practice
After studying First Law of Thermodynamics, you should be able to: (1) define the main quantities, (2) select the correct relation, (3) solve typical numericals, and (4) interpret results physically — not just substitute numbers.
Key relations & formulas
(differential form, P.K. Nag sign convention)
(finite process, closed system)
Notation and sign conventions
Relation 1 —
(differential form, P.K. Nag sign convention)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
(finite process, closed system)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Fundamentals and definitions
1. State function: U — path independent For first law of thermodynamics problems in Thermodynamics, this directly affects how you set up the solution and what you check in the final answer.
Governing relations in practice
2. Work W: +ve when done BY system For first law of thermodynamics problems in Thermodynamics, this directly affects how you set up the solution and what you check in the final answer.
Design and analysis considerations
3. Heat Q: +ve when added TO system For first law of thermodynamics problems in Thermodynamics, this directly affects how you set up the solution and what you check in the final answer.
Assumptions and validity limits
State assumptions explicitly before using any relation for first law of thermodynamics — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Thermodynamics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Thermodynamics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to first law of thermodynamics.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to first law of thermodynamics.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
First Law of Thermodynamics appears in engines, boilers, and refrigeration cycles. In Indian mechanical curricula this topic is tested because it connects theory to energy, heat, and work in thermal systems.
GATE and semester exams often combine first law of thermodynamics with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use first law of thermodynamics?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
Avoid these traps in Thermodynamics exams:
• Rushing to the calculator without a labelled diagram or sign convention
• Mixing units (mm vs m, kN vs N, kW vs W)
• Skipping intermediate steps — step marks matter in Indian university papers
• Applying a relation from first law of thermodynamics outside its valid assumptions
• Mixing units (mm vs m, kN vs N, kW vs W)
• Skipping intermediate steps — step marks matter in Indian university papers
• Applying a relation from first law of thermodynamics outside its valid assumptions
Textbook focus: P.K. Nag Ch. 4 — practice closed system and control volume forms.
Quick revision checklist
Before attempting first law of thermodynamics problems, confirm you can:
1. State function: U — path independent
2. Work W: +ve when done BY system
3. Heat Q: +ve when added TO system
2. Work W: +ve when done BY system
3. Heat Q: +ve when added TO system
Revise the solved examples in Engineering Thermodynamics — P.K. Nag and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Guided practice — First Law of Thermodynamics
Problem
A standard Thermodynamics numerical on first law of thermodynamics supplies given data in SI units. Using δQ = dU + δW and Q − W = ΔU, find the unknown quantity and state whether the result is physically reasonable.
Solution
1. List all given quantities with units (convert to SI if needed).
2. Draw a neat labelled diagram — diagram marks are common in Indian B.Tech papers.
3. Select
4. Substitute values, compute, and attach correct units.
5. Sanity-check: magnitude, sign, and direction must match energy, heat, and work in thermal systems.
2. Draw a neat labelled diagram — diagram marks are common in Indian B.Tech papers.
3. Select
and write it symbolically before substitution.
4. Substitute values, compute, and attach correct units.
5. Sanity-check: magnitude, sign, and direction must match energy, heat, and work in thermal systems.
Reference: P.K. Nag Ch. 4 — practice closed system and control volume forms.
Conceptual check — First Law of Thermodynamics
Problem
In a Thermodynamics semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of first law of thermodynamics." What should a complete answer include?
Practice questions
Most-asked interview and GATE questions for this topic — expand any item for a model answer.
- 1What is First Law of Thermodynamics, and why does it appear in B.Tech / GATE syllabi?
Model answer
First Law of Thermodynamics is a core unit linking theory to numerical problem-solving. Focus on definitions, governing relations, and valid assumptions. - 2State the relation δQ = dU + δW and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 3State the relation Q − W = ΔU and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 4Explain: State function: U — path independent
Model answer
State function: U — path independent — state the assumption range and one exam trap linked to this point. - 5Explain: Work W: +ve when done BY system
Model answer
Work W: +ve when done BY system — state the assumption range and one exam trap linked to this point. - 6Explain: Heat Q: +ve when added TO system
Model answer
Heat Q: +ve when added TO system — state the assumption range and one exam trap linked to this point. - 7List three assumptions you must state before applying first law of thermodynamics formulas.
Model answer
Typical assumptions include continuum/idealised geometry, constant properties (or stated means), and the loading/flow regime implied by the derivation. Always match the textbook statement for the specific relation. - 8How do you present a full-mark numerical solution for First Law of Thermodynamics?
Model answer
Given data with units → labelled diagram → symbolic equation → substitution → boxed answer with units → one-line physical check. - 9Name one practical application of First Law of Thermodynamics you can mention in an interview.
Model answer
Connect first law of thermodynamics to a lab, mini-project, or plant example (machine, structure, thermal system, or process) and state which formula you used. - 10What diagram or sketch earns marks for First Law of Thermodynamics in university papers?
Model answer
A neat free-body / schematic with labelled forces, temperatures, velocities, or sections as applicable — even a simple sketch often carries separate marks. - 11How would you check whether your first law of thermodynamics answer is physically reasonable?
Model answer
Check order of magnitude, sign/direction, limiting cases (zero load, infinite stiffness, etc.), and unit consistency.
Exams & GATE
P.K. Nag Ch. 4 — practice closed system and control volume forms.
📖 Standard books (India)
Engineering Thermodynamics — P.K. Nag
Read: Syllabus unit
The standard thermodynamics text in most Indian universities
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