THM-31

Isentropic p–T

Reversible adiabatic ideal gas.

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GoverningIsentropic p–T

Governing equation

T_2=T_1(p_2/p_1)^{(\gamma-1)/\gamma}

where

T1: T1 (K)
p1: p1 (kPa)
p2: p2 (kPa)
g: g (—)
T2: Isentropic p–T (K)

Lecture brief

Historical brief

Carnot (1824), Clausius entropy, the first law and later van der Waals and Gibbs potentials turned heat into a state science. The sheets compute work, efficiency and vapour pressure. This sheet (THM-31 — Isentropic p–T) is the form associated with Isentropic p–T. Working symbols: $T1$ , $p1$ , $p2$ , $g$ $\rightarrow$ $T2$ . Reversible adiabatic ideal gas. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

T2

from

T1

p1

p2

g

in Thermodynamics via

T_2=T_1(p_2/p_1)^{(\gamma-1)/\gamma}

Reversible adiabatic ideal gas. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

T1 = 300.000\,\mathrm{K}

p1 = 100.000\,\mathrm{kPa}

p2 = 800.000\,\mathrm{kPa}

g = 1.400\,\mathrm{—}

, the governing relation

T_2=T_1(p_2/p_1)^{(\gamma-1)/\gamma}

yields

T2 = 543.434\,\mathrm{K}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

T1 T1300 Kp1 p1100 kPap2 p2800 kPag g1.4 —

Outputs

Isentropic p–T T2543.434 K

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Reversible adiabatic ideal gas. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube