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In addition, although isothermal compression cannot be achieved in practice, it is often used as a basis for compression with other compression processes. The effect of the amount of coolers on the compression force or power will be covered under Polytropic Compression.
Isothermal Process and the First Law
The classical form of the first law of thermodynamics is the following equation:
dU = dQ – dW
In this equation, dW is equal to dW = pdV and is known as the boundary work.
In the isothermal process and the ideal gas, all heat added to the system will be used to do work:
Isothermal process (dU = 0):
dU = 0 = Q – W → W = Q (for ideal gas)
First Law | dU=0dQ=dW |
Ideal Gas Relation | pV=constant |
P,V,T Relations | P1V1=P2V2 |
Change in Internal Energy | dU=0 |
Change in Enthalpy | dH=0 |
Heat Transfer | Q=nRT ln(Vf/Vi)Q=piVi ln(Vf/Vi) Where n= number of moles R=Universal gas Constant T= Temperature Vf=final volume Vi=initial volume |
pdV Work | Wi->f=nRT ln(Vf/Vi)Wi->f=piVi ln(Vf/Vi) n= number of moles R=Universal gas Constant T= Temperature Vf=final volume Vi=initial volume |
Isothermal Expansion Isothermal Compression
In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.
pV = nRT
where:
p is the absolute pressure of the gas
n is the amount of substance
T is the absolute temperature
V is the volume
R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,
In this equation the symbol R is a constant called the universal gas constant that has the same value for all gases—namely, R = 8.31 J/mol K.
The isothermal process can be expressed with the ideal gas law as:
pV = constant
p1V1 = p2V2
On a p-V diagram, the process occurs along a line (called an isotherm) that has the equation p = constant / V.
Boyle–Mariotte Law
Boyle-Mariotte Law is one of the gas laws. At the end of the 17th century, Robert William Boyle and Edme Mariotte independently studied the relationship between the volume and pressure of a gas at a constant temperature. The results of certain experiments with gases at relatively low pressure led Robert Boyle to formulate a well-known law. It states that:
For a fixed mass of gas at a constant temperature, the volume is inversely proportional to the pressure.
That means that, for example, if you increase the volume 10 times, the pressure will decrease 10 times. If you halve the volume, you will double the pressure.
Examples of Isothermal Processes
Isothermal processes can occur in any type of system that has some means of regulating temperature. Below we list some examples:
- The phase changes of different liquids through the melting and evaporation process are isothermal.
- Certain cycles of heat engines; for instance, Carnot’s machine. Part of the Carnot cycle is performed and the temperature remains constant.
- Reactions in the refrigerator are isothermal and a constant temperature is maintained.
- In biology, the interactions of a cell with its surrounding cells are done through isothermal processes.
