Physics Mr. Jongie G. Gepulgani

The General Gas Law

The General Gas Law Sample Problem: A tank of helium gas has a gage pressure of 50.02 lbs/in2 and a temperature of 45˚F. A piston decreases the volume of the gas to 68% of its original volume and the temperature drops to 10˚F. What is the new gage pressure? Assume normal atmospheric pressure.

The General Gas Law The Solution: Change temperatures and pressure to absolute values. Hence,

The General Gas Law The Solution: while Substituting all converted values: Then:

The Alternate Form of the General Gas Law The General Gas Law tells us that for a fixed quantity of gas, the expression PV/T is constant. Since PV/T is a constant for a fixed mass of gas, we can set this expression equal to the product of the mass(m) of the gas and what is referred to as a gas constant (R). This gas constant (R) varies according to the type of gas.

The Alternate Form of the General Gas Law The table below shows the values for (R). Air 0.287 1710 Carbon dioxide 0.189 1130 Helium 2.077 12,380 Nitrogen 0.297 1770 Oxygen 0.260 1550 Water Vapor 0.462 2760

The Alternate Form of the General Gas Law Hence, But the density of any substance is given by:

The Alternate Form of the General Gas Law Therefore we can write: Thus, the density of any particular kind of gas if we know the absolute pressure and absolute temperature is given in the following formula:

The Alternate Form of the General Gas Law Sample problem: Find the density of air if the temperature is 800F and the absolute pressure is 2,150 lbs/ft2.

The Application of the General Gas Law to Compressors We can apply the general gas law to the flow of air through the compressor of a turbojet engine. The function of the compressor is to provide a large quantity of high pressure air to the limited space of the combustion chamber. The reason for this is that the energy released in the combustion chamber is proportional to the mass of air consumed. The pressure of the air when it leaves the compressor is called the compressor discharge pressure (CDP).

The Application of the General Gas Law to Compressors And the ratio of this to the compressor inlet pressure (CIP) is the compression ratio. Or it can be expressed as: Where the 1s refer to the inlet pressure and the 2s refer to the discharge pressure.

The Application of the General Gas Law to Compressors Air entering a compressor having a compression ratio of 12.5:1 at a pressure of 14.7 PSIA will leave with a pressure of: The above conversion is invalid for a change in temperature.

The Application of the General Gas Law to Compressors Sample problem: A quantity of air occupying 1 cu ft at a pressure of 14.7 PSIA and a temperature of 590F enters the compressor of a turbojet engine having a compression ratio 12.5:1 and is discharged at a temperature of 2,0000F. With what volume will this quantity of air enter the combustion chamber?

The Application of the General Gas Law to Compressors The solution: From the general equation: Solving for V2 we get:

The Application of the General Gas Law to Compressors The solution: Substituting the values to the preceding equation:

Exercises 1. A dirigible is filled with helium gas. The volume of the balloon is 25,700 ft3 , the absolute pressure is 14.9 lbs/in2. And the temperature is 870F. The balloon later experiences an absolute pressure 14.1 lbs/in2 and simultaneously a temperature of 450F. What is the new volume of this balloon?

Exercises 2. At an altitude of 8,000 ft., the absolute temperature of air is 4900R and the absolute pressure is 1572lbs/ft2. What is the density of air at this altitude?

Exercises 3. A quantity of air occupying 0.9ft3 at a pressure of 14.7 PSIA and a temperature of 400F enters the compressor of a turbojet engine having a compression ratio of 13:1 and is discharged at a temperature of 1,9000F. With what volume will this quantity of air enter the combustion chamber?

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