---
title: "Functions and energy equations of steady-flow devices"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 4
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:turbine-compressor-nozzle-hx-functions"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/turbine-compressor-nozzle-hx-functions
site: BCT Engineering
---

# Functions and energy equations of steady-flow devices

Fundamental of Thermodynamics & Heat Transfer · Chapter 4: First Law of Thermodynamics

- Asked in: 2073 Magh, 6 marks
- Video: [Steady Flow Energy Equation](https://www.youtube.com/watch?v=6VA6A_qJjCs) — BEST MECHANICAL ENGINEERING
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/turbine-compressor-nozzle-hx-functions
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-4

## Question

Write down the functions of turbine, compressor, nozzle and heat exchanger. Also write down energy equations for them.

## Short answer

Turbine: produces work from enthalpy drop, adiabatic w = h1 - h2. Compressor: uses work to raise pressure, adiabatic w_in = h2 - h1. Nozzle: converts enthalpy to kinetic energy, h1+V1²/2 = h2+V2²/2. Heat exchanger: transfers heat between streams, ṁ_h(h_h,in - h_h,out) = ṁ_c(h_c,out - h_c,in).

## Answer

All of these are steady flow devices: ṁ_in = ṁ_out, and the steady-flow energy equation is  
Q̇ − Ẇ = Σṁ_e (h + V²/2 + gz)_e − Σṁ_i (h + V²/2 + gz)_i

| Device | Function | Energy equation (per unit mass, ΔPE ≈ 0) |
|---|---|---|
| Turbine | Expands steam/gas, converting enthalpy to shaft work output | w = (h₁ − h₂) + (V₁² − V₂²)/2 + q; adiabatic and ΔKE ≈ 0: w = h₁ − h₂ |
| Compressor (also pump, fan) | Raises the pressure of a gas using shaft work input | w_in = (h₂ − h₁) + (V₂² − V₁²)/2 − q; adiabatic: w_in = h₂ − h₁ |
| Nozzle | Increases the velocity of the fluid by decreasing its pressure | h₁ + V₁²/2 = h₂ + V₂²/2 (Q = W = 0), V₂ = √(V₁² + 2(h₁ − h₂)) |
| Heat exchanger | Transfers heat between two fluid streams without mixing (condenser, boiler, radiator) | ṁ_h (h_h,in − h_h,out) = ṁ_c (h_c,out − h_c,in) (W = 0, no loss to surroundings) |

**Example:** in a steam power plant, steam from the boiler expands in the turbine (work out), the exhaust is condensed in the condenser (a heat exchanger), and a pump raises the pressure of the liquid. Nozzles are used in jet engines and in steam turbines, where they direct high-velocity steam onto the blades.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A compressor:
   A. Raises the pressure of a gas using shaft work input
   B. Produces work from a gas
   C. Increases velocity via pressure drop
   D. Exchanges heat between streams
   Answer: A. Adiabatic: w_in = h2 - h1. (Key point: Compressor)

2. Nozzle energy equation:
   A. h1 = h2 + w
   B. h1 + V1²/2 = h2 + V2²/2
   C. h2 - h1 = w
   D. h1 = h2
   Answer: B. Q = W = 0. (Key point: Nozzle)

3. Heat exchanger energy balance:
   A. W = ṁ(h1 - h2)
   B. ṁ_h = 0
   C. ṁ_h(h_h,in - h_h,out) = ṁ_c(h_c,out - h_c,in)
   D. h_in = h_out for each stream
   Answer: C. Heat lost by hot stream equals heat gained by cold stream. (Key point: Heat exchanger)

4. The turbine converts:
   A. Shaft work into pressure
   B. Kinetic energy to heat
   C. Heat into mass
   D. Enthalpy of the fluid into shaft work
   Answer: D. w = h1 - h2 for adiabatic, negligible KE. (Key point: Turbine)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Steady state work vs steady flow; turbine, nozzle](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteady-state-work-vs-flow) — Fundamental of Thermodynamics & Heat Transfer, chapter 4
- [Mass and energy equations for CV; nozzle, condenser](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Amass-energy-cv-nozzle-condenser) — Fundamental of Thermodynamics & Heat Transfer, chapter 4
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- [Mass and energy equations for non-flow; cyclic process](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Amass-energy-nonflow-cyclic-closed) — Fundamental of Thermodynamics & Heat Transfer, chapter 4
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- [Steam nozzle 4 MPa: mass flow, exit velocity, area](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteam-nozzle-4mpa-450c-to-2mpa) — Fundamental of Thermodynamics & Heat Transfer, chapter 4

## Related in other subjects

- [Heat exchanger types and LMTD derivation](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aclassification-heat-exchangers-lmtd-derivation) — Heat Transfer, chapter 6
- [Effectiveness-NTU analysis of a heat exchanger](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aeffectiveness-ntu-counterflow-oil-water) — Heat Transfer, chapter 6
- [Compressor and turbine performance characteristics](https://www.bctengineer.com/question.md?key=semester_7%2Fturbo_machines%3Acompressor-turbine-performance-characteristics) — Turbo Machines, chapter 3
- [Gas turbine nozzle: principle and types](https://www.bctengineer.com/question.md?key=semester_7%2Fturbo_machines%3Anozzle-principle-types) — Turbo Machines, chapter 4