Order of Work Done in Ideal Gas Compression Processes

Introduction: In thermodynamics, the amount of work done during a gas compression process depends on the type of process and its conditions. There are four main types of compression processes: isothermal, adiabatic, isobaric, and isochoric. In this article, we will discuss the correct decreasing order of work done in each of these processes for an ideal gas.

Isothermal Process: In an isothermal process, the temperature of the gas remains constant. Therefore, the work done during this process is given by the formula:

W = nRTln(V2/V1)

where W is the work done, n is the number of moles of gas, R is the gas constant, T is the temperature, and V1 and V2 are the initial and final volumes of the gas, respectively.

Adiabatic Process: In an adiabatic process, there is no heat transfer between the system and its surroundings. Therefore, the work done during this process is given by the formula:

W = (nCv)(T1-T2)

where W is the work done, n is the number of moles of gas, Cv is the specific heat capacity at constant volume, and T1 and T2 are the initial and final temperatures of the gas, respectively.

Isobaric Process: In an isobaric process, the pressure of the gas remains constant. Therefore, the work done during this process is given by the formula:

W = P(V2-V1)

where W is the work done, P is the constant pressure, and V1 and V2 are the initial and final volumes of the gas, respectively.

Isochoric Process: In an isochoric process, the volume of the gas remains constant. Therefore, no work is done during this process.

Decreasing Order of Work Done: Based on the above formulas, we can conclude that the correct decreasing order of work done for an ideal gas in each process is:

1. Isothermal (W1)
2. Isobaric (W3)
3. Adiabatic (W2)
4. Isochoric (W4)

This is because the work done in an isothermal process is the highest, followed by isobaric, adiabatic, and isochoric processes where no work is done.

Conclusion: The amount of work done during an ideal gas compression process depends on the type of process and its conditions. The order of work done for an ideal gas in each process is isothermal, isobaric, adiabatic, and isochoric, respectively.

W3>w1>w2>w4 .