Question

3. An ideal gas is initially at a certain pressure and volume. It expands until its volume is four times the initial volume. This is done through an isobaric, an isothermal, and an adiabatic process, respectively. During which of the processes …. a) …is the work done by the gas greatest? b) … is the smallest amount of work done by the gas? c) … does the internal energy increase? d) …does the internal energy decrease? e)… does the largest amount of heat flow into the gas? Hint: You may want to sketch a p-V diagram.

Answer 1

The gas does work on the outside world, as this force moves the piston through some distance. Heat transfer to the gas cylinder results in work being done. To repeat this process, the piston needs to be returned to its starting point. Heat transfer now occurs from the gas to the surroundings so that its pressure decreases, and a force is exerted by the surroundings to push the piston back through some distance. Variations of this process are employed daily in hundreds of millions of heat engines. We will examine heat engines in detail in the next section. In this section, we consider some of the simpler underlying processes on which heat engines are based.

Answer 2

(a) For the work done by the ideal gas from greatest to the least; isobaric (1) >  isothermal (2) > adiabatic process (3).

(b)  For the change in internal energy of the ideal gas from greatest to the least; adiabatic process (3) > isothermal (2) > isobaric (1)

Work done by the gas

The work done by the gas can be determined from the area under the pressure volume curve.

Area under the curve

The area for curve 1 at constant pressure (isobaric) is the greatest

Let the slope of the curve = M

M₂ = γM₃

where;

• γ is constant for adiabatic process

The slope of curve 2 is bigger that slope of curve 3 (M₂ > M₃), thus area of curve2 is bigger than curve 3.

Thus, we can conclude the following for work done by the gas;

isobaric (1) >  isothermal (2) > adiabatic process (3)

Change in internal energy of the gas

The change in the internal energy of the gas is determined from first law of thermodynamics;

ΔU = Q - W

where;

• Q is heat added to the gas
• W is work done by the gas

ΔU = -W

The process with then highest work done will be the least change in internal energy while the process with the least work done will be the highest change in internal energy.

For change in internal energy;

adiabatic process (3) > isothermal (2) > isobaric (1)

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