# Work done by product gas in reversible adiabatic expansion

• Egbert
In summary, the conversation discusses calculating the work done by a product gas in reversible adiabatic expansion and the final temperature. The equation PVγ = constant is mentioned, along with the assumption of Cv = constant and the relationship gamma = cv + nR / Cv. The suggestion is made to substitute one equation into the other and integrate, with the question of whether to assume a P1 value of 1 bar. The parameters of the gas in its initial state are also discussed, including the combustion reaction of ethanol, the initial volume, and the initial number of moles of gas and temperature. The ideal gas law is brought up as a possible way to calculate the initial pressure.
Egbert
posted in general physics forum, please wait for OP to show work
I am having trouble calculating the work done by a product gas in reversible adiabatic expansion, and in calculating the final temperature. pV gamma = constant, Cv = constant (assume), gamma = cv + nR / Cv.
anyone who can help me out?

Work done = ∫P.dV
PVγ = P1V1γ = P2V2γ

Try substituting one equation in the other and integrating from V1 to V2

I only know the V1, V2 and n. Should this work or should I assume a P1 of 1 bar?

What parameters do you know about the gas in its initial state before the expansion?

Chet

I
Chestermiller said:
What parameters do you know about the gas in its initial state before the expansion?

Chet
t is a combustion reaction of ethanol, volume is increasing from 0.02 m3 to 0.04 m3 with a starting temperature of 4000 K. Also the amounts are known. (12g ethane and enough oxygen)
Thanks

Egbert said:
I

t is a combustion reaction of ethanol, volume is increasing from 0.02 m3 to 0.04 m3 with a starting temperature of 4000 K. Also the amounts are known. (12g ethane and enough oxygen)
Thanks
You know the initial volume, the initial number of moles of gas, and the initial temperature. From the ideal gas law, what do you get for the initial pressure?

Chet

Using PV = nRT and PVγ = constant, can you devise an equation with 'V' and 'T'?

## 1. What is reversible adiabatic expansion?

Reversible adiabatic expansion is a thermodynamic process in which a gas expands without any heat exchange with its surroundings. This means that the gas expands and its temperature decreases, but there is no heat added or removed from the system.

## 2. How is work done by product gas calculated in reversible adiabatic expansion?

The work done by product gas in reversible adiabatic expansion is calculated using the formula W = -PΔV, where P is the pressure of the gas and ΔV is the change in volume of the gas during the expansion process.

## 3. Why is reversible adiabatic expansion important in scientific research?

Reversible adiabatic expansion is important in scientific research because it allows us to understand the behavior of gases and their thermodynamic properties. It also has practical applications in various industries, such as in the production of compressed gases and refrigeration systems.

## 4. What is the difference between reversible and irreversible adiabatic expansion?

The main difference between reversible and irreversible adiabatic expansion is that reversible expansion is a theoretical process that occurs without any energy loss, while irreversible expansion involves some energy loss due to friction and other factors. Reversible expansion also follows the laws of thermodynamics, while irreversible expansion does not.

## 5. How does reversible adiabatic expansion relate to the first law of thermodynamics?

Reversible adiabatic expansion is an example of a process that follows the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted. In this process, the change in internal energy of the gas is equal to the work done by the gas, as there is no heat exchange involved.

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