Question

Question about Quasi- static process

From the answers given there, what I understood is this: After irreversible adiabatic compression and expansion, even though the final pressure is same as initial pressure, final temperature of the gas is not the same as initial temperature. The final temperature will be more because more work has to be done by surroundings in compression than done by the gas in expansion.
a) More work is done during compression because more weight is placed on the piston (two weights) during compression than expansion( only one weight is removed). So more work is transferred to the system during compression and then this work adds to system's internal energy, hence the temperature increase. Is this correct?
b) When one of the weights is reduced( for expansion), the pressure on the piston drops suddenly and the piston shoots up, so there will be temperature gradients inside the gas, which will give rise to entropy, hence making the process irreversible.

Answer 1

The student's understanding that irreversible adiabatic compression increases gas temperature due to work being added to the system's internal energy is correct. Sudden weight removal during expansion increases entropy and causes irreversibility. These concepts distinguish adiabatic from isothermal processes, where the temperature remains constant through heat transfer.

Step-by-step explanation:

The question at hand involves understanding adiabatic processes in thermodynamics, particularly in the context of gas compression and expansion. The student correctly identifies that for an irreversible adiabatic compression where more work is done on the gas (due to increased external pressure from adding more weights), the internal energy of the gas increases and so does its temperature. This rise in temperature is due to the work being converted to internal energy, as no heat transfer occurs in an adiabatic process.

On the other hand, in an adiabatic expansion with a sudden removal of weight, the pressure drops, causing the gas to expand quickly, which can create temperature gradients and increase entropy. This increase in entropy, along with the fact that the process is not carried out infinitely slowly, contributes to the irreversibility of the process.

Correctly, the student also distinguishes between an adiabatic process and an isothermal process, where in the latter, the temperature remains constant due to heat exchange with the surroundings, whereas in the former, any change in internal energy and, consequently, temperature, is solely due to work done on or by the system.

Answer 2

During irreversible adiabatic compression and expansion, the final temperature of the gas is not the same as the initial temperature. More work is done on the gas during compression, leading to an increase in temperature. The expansion process becomes irreversible due to temperature gradients inside the gas.

Step-by-step explanation:

a) More work is done during compression because more weight is placed on the piston during compression than during expansion (only one weight is removed). So more work is transferred to the system during compression, and then this work adds to the system's internal energy, hence the temperature increase. Is this correct?

This explanation is not entirely accurate. The work done on or by gas during compression or expansion is determined by the area under the pressure-volume (P-V) curve on a thermodynamic diagram. In an irreversible adiabatic compression, the process is not efficient, and more work might be done on the gas compared to an ideal (reversible) process. The increase in internal energy is related to the work done on the gas and is manifested as a temperature increase.

So, the key point here is that during an irreversible adiabatic compression, more work is done on the gas, leading to an increase in internal energy and, consequently, an increase in temperature. This is not directly related to the number of weights on the piston but rather to the nature of the process.

b) When one of the weights is reduced (for expansion), the pressure on the piston drops suddenly, and the piston shoots up. There will be temperature gradients inside the gas, which will give rise to entropy, hence making the process irreversible.

This explanation is closer to the correct understanding. In an irreversible expansion, sudden changes in pressure and volume can lead to non-uniformities or gradients in temperature within the gas. These gradients contribute to entropy generation, making the process irreversible. The irreversibility is associated with the lack of equilibrium and the departure from a quasi-static process.