Ideal Gas Law
Pressure, volume and temperature, are all related.
The combined gas law is an equation based upon the ideal gas law equation. The combined gas law states:
|
Fuel Oil |
Average Heating Value (imperial unites) |
Average Heating Value (metric units) |
|
No. 1 Kerosene |
134,000 Btu/gal |
37.34 MJ/l |
|
No. 2 Burner Fuel Oil |
140,000 Btu/gal |
39.02 MJ/l |
|
No. 4 Heavy Fuel Oil |
144,000 Btu/gal |
40.13 MJ/l |
|
No. 5 Heavy Fuel Oil |
150,000 Btu/gal |
41.80 MJ/l |
|
No. 6 Heavy Fuel Oil (2.7% sulphur) |
152,000 Btu/gal |
42.36 MJ/l |
|
No. 6 Heavy Fuel Oil (0.3% sulphur) |
143,800 Btu/gal |
40.07 MJ/l |
|
Coal |
Average Heating Value (imperial unites) |
Average Heating Value (metric units) |
|
Anthracite |
13,900 Btu/lb |
32.3 MJ/kg |
|
Bituminous |
14,000 Btu/lb |
32.6 MJ/kg |
|
Sub-bituminous |
12,600 Btu/lb |
29.3 MJ/kg |
|
Lignite |
11,000 Btu/lb |
25.6 MJ/kg |
|
Gas |
Average Heating Value (imperial unites) |
Average Heating Value (metric units) |
|
Natural |
1,000 Btu/cu ft |
37.3 MJ/m3 |
|
Liquefied Butane |
103,300 Btu/gal |
28.79 MJ/l |
|
Liquefied Propane |
91,600 Btu/gal |
25.53 MJ/l |
Fuel Heat Value Table
Where:
P = Pressure
V = Volume
T = Temperature
k = Constant for a fixed amount of gas.
P, V and T, are termed variables, because they vary (vary-able) depending upon real world factors that are then entered as values into the equation. The ratio of PV to T is constant. This means that as P increases, V decreases, and as V increases, P decreases. The relationship between pressure and volume at constant temperature is inversely proportional.
If temperature is held constant, an increase in pressure will be accompanied by a decrease in volume.
If temperature is held constant, a decrease in pressure will be accompanied by an increase in volume.
If P is held at the same value, then V and T are directly related i.e. if V increases then T increases, and vice versa. The same situation occurs if V is held constant i.e. P and T are related, and an increase in P will cause an increase in T, and vice versa. The relationship between temperature and pressure at constant volume is linear, as is the relationship between temperature and volume at constant pressure.
A few examples without units can be used to clarify the equation further.
Example 1
A steam system has a pressure of 10, volume of 3 and temperature of 100.
A steam system’s volume is fixed, as it is a closed system. Increasing the system pressure to 15 must also proportionally increase the temperature because the constant value (k) must be maintained in order for the equation to be valid. It is possible to calculate T, by inputting the new higher-pressure value of 15 then solving the equation.
P = 15
V = 3
K = 0.3
T = ?
PV / T = k
(15 x 3) / T = 0.3
(15 x 3) / 0.3 = T
(15 x 3) / 0.3 = 150
Similarly, a reduction in pressure will lead to a reduction in temperature because the volume is held constant.
If volume is held constant, an increase in pressure will be accompanied by a proportional increase in temperature.
If volume is held constant, a decrease in pressure will be accompanied by a proportional decrease in temperature.
The ideal gas law is used to calculate pressures, volumes and temperatures of a gas across various ranges. Once these values are known, its possible to calculate things such as:
- The amount of energy the system contains and how much can be transferred to the point of use e.g. to a steam turbine.
- The size and thickness of system piping required.
- The size of boilers required.
- Gas velocity within the system.
Some of this data is then tabulated in a gas table, or when used for steam, a steam table. Steam tables are essential when designing and operating a steam system.
Additional Resources
https://en.wikipedia.org/wiki/Ideal_gas_law
https://www.sciencedirect.com/topics/engineering/ideal-gas-law
https://chem.libretexts.org/Bookshelves