# 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]

where

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

T2=298(17/1)[1-1/1.4]

T2=670K

Source:

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

# 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,
w=work.

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.

Source:

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

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