Thermodynamics: Compression of an Adiabatic Gas

• Minescrushessouls
In summary, assuming 1.500 mol of a monatomic ideal gas is compressed from 3.00 L to 1.00 L at a constant temperature of 10.0 °C, the initial and final pressures are 11.6 atm and 34.8 atm, respectively. The work input required for a reversible isothermal path at 10.0 °C is 3.88 kJ. For an adiabatic compression at the same initial temperature, the work input can be calculated using the equation ΔU = -PΔV, where U is the internal energy, and q = 0.
Minescrushessouls

Homework Statement

Assume 1.500 mol of a monatomic ideal gas is compressed from 3.00 L to 1.00 L.

a. If the initial and final temperature is 10.0 °C, what are the initial and final pressures (in atm)?

b. How much work input (in kJ) is required if a reversible isothermal path at 10.0 °C is followed?

c. How much work input (in kJ) is required if the compression is adiabatic rather than isothermal? Assume the initial temperature is 10.0 °C.

PV=nRT
w=-nRTln(vf/vi)
U=q+w

The Attempt at a Solution

I got both a and b using the first two equations I listed. I got the inital pressure to be 11.6 atm and the final pressure to be 34.8 atm. For the second part I got the work to be 3.88 kJ.

I'm stuck on the third part. I know adiabatic means that there no change in U, so q=-w but I don't know how that applies to the question.

You're missing an equation for the energy U of an ideal gas. And adiabatic does not mean ΔU = 0, it means q = 0.

So ΔU=-PΔV, where U=w

But the problem isn't isobaric, so that equation wouldn't work. I can't seem to find another equation though...

1. What is thermodynamics?

Thermodynamics is a branch of physics that studies the relationship between heat, energy, and work. It also examines how these factors affect the state and behavior of matter.

2. What is the compression of an adiabatic gas?

The compression of an adiabatic gas refers to the process of reducing the volume of a gas without any heat transfer to or from the surroundings. This means that the gas is compressed without any energy being added or removed.

3. How does compression affect an adiabatic gas?

Compression of an adiabatic gas leads to an increase in temperature and pressure, as the gas molecules are squeezed into a smaller space. This causes the gas to become more energetic and collide more frequently, resulting in an increase in temperature and pressure.

4. What is the adiabatic index?

The adiabatic index, also known as the heat capacity ratio, is a thermodynamic property that describes the relationship between the specific heat capacities at constant pressure and constant volume for a given gas. It is denoted by the symbol γ and is typically around 1.4 for most gases.

5. What is the adiabatic process?

The adiabatic process is a thermodynamic process in which no heat is exchanged between a system and its surroundings. This means that the internal energy of the system remains constant, and any changes in temperature and pressure are a result of work being done on or by the system.

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