Chemistry, thermodynamics: temperature increase caused by compression, continued

The tutor looks more specifically into the effect of compression on gas temperature.

In my January 20 post I began about thermodynamics and the effect of compressing a gas. Today, I’ll give more specific coverage.

The temperature rise a gas experiences (without change in entropy) due to pressure is given by the formula

T2 = T1(P2/P1)[1-1/γ]


T1,T2 are initial and final temperatures

P1,P2 are initial and final temperatures

γ = Cp/Cv, where

Cp = gas specific heat at constant pressure

Cv = gas specific heat at constant volume

Typcially, γ might be around 1.4. Therefore, imagining a diesel engine with 17:1 compression, at starting temperature 298K (25°C) the resulting temp, T2, might be




Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Thermodynamics: first law, with compression of a gas

The tutor begins about thermodynamics with the example of compressing a gas.

Thermodynamics is the analysis of energy – particularly, how it moves and/or changes form. The First Law of Thermodynamics is the Law of Conservation of Energy: Energy cannot be created or destroyed, but merely moves or changes form.

Let’s imagine a system that has internal energy U. Then U can change only by work or heat (Δ means change):

ΔU = q + w,

q= heat,

If q is negative, heat is leaving the system; if w is negative, the system is doing work against its environment.

The internal energy of an ideal gas is directly proportional to its temperature: specifically,

U = 1.5nRT, where

n= moles of gas present
R=8.315J/(K*mol), which is the gas constant
T=temperature in Kelvin

As a gas is compressed, work is done to it (so w is positive). Let’s imagine rapid compression that does not allow time for heat to escape, so q=0. Then according to

ΔU = q + w,

U must increase. Since

U = 1.5nRT

the temperature of the (ideal) gas must rise with compression.

The rise of temperature during compression enables diesel engines and refrigerators to work.


Giancoli, Douglas C. Physics, 5th ed. New Jersey: Prentice Hall, 1998.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.