---
title: "Define critical point, quality, enthalpy, cv of ideal gas"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 3
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:critical-point-quality-enthalpy-cv-defs"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/critical-point-quality-enthalpy-cv-defs
site: BCT Engineering
---

# Define critical point, quality, enthalpy, cv of ideal gas

Fundamental of Thermodynamics & Heat Transfer · Chapter 3: Properties of Common Substances

- Asked in: 2071 Magh, 4 marks
- Video: [T-v Diagrams and PROPERTY TABLES for Thermodynamics in 13 Minutes!](https://www.youtube.com/watch?v=iZbnY0QWHe8) — Less Boring Lectures
- 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/critical-point-quality-enthalpy-cv-defs
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-3

## Question

Define the following terms: critical point, quality, enthalpy, specific heat of an ideal gas at constant volume.

## Short answer

Critical point: saturated liquid and vapor become identical, top of dome (22.09 MPa, 374.1°C). Quality x = m_g/m. Enthalpy H = U+PV (h = u+Pv). cv = (∂u/∂T)_v; for ideal gas du = cv dT (air 0.718 kJ/kg·K).

## Answer

- **Critical point:** the state at which saturated liquid and saturated vapour become identical; it lies at the top of the saturation dome. For water: P_c = 22.09 MPa, T_c = 374.1 °C. At pressures above P_c there is no distinct boiling.
- **Quality (dryness fraction), x:** the mass of vapour divided by the total mass of a liquid-vapour mixture, x = m_g/m (0 ≤ x ≤ 1). It is used in v = v_f + x v_fg.
- **Enthalpy:** a property defined by H = U + PV (kJ); per unit mass, h = u + Pv. It is the energy carried by a flowing fluid per unit mass (internal energy plus flow work), and its change equals the heat transferred in a reversible constant-pressure process.
- **Specific heat of an ideal gas at constant volume (c_v):** the heat required to raise the temperature of unit mass of the gas by 1 K at constant volume: c_v = (∂u/∂T)_v. For an ideal gas du = c_v dT; for air c_v = 0.718 kJ/kg·K.

## Check yourself

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

1. At the critical point:
   A. Quality is 0.5
   B. Saturated liquid and vapour become identical
   C. Ice melts
   D. T is 100 C
   Answer: B. Water: 22.09 MPa, 374.1 C. (Key point: Critical point)

2. Quality x is:
   A. Volume of vapour / total volume
   B. Mass of liquid / total
   C. Mass of vapour / total mass
   D. Pressure ratio
   Answer: C. It is used with v = vf + x vfg. (Key point: Quality)

3. Enthalpy is:
   A. H = U - PV
   B. H = PV
   C. H = Q
   D. H = U + PV
   Answer: D. Also the heat transferred at constant pressure. (Key point: Enthalpy)

4. For an ideal gas du equals:
   A. cv dT
   B. cp dT
   C. P dv
   D. T ds
   Answer: A. cv = (du/dT)v; for air 0.718 kJ/kg K. (Key point: cv ideal gas)

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