Order the follow processes from (1) the least work done by the system to (5) the most work done by one mole of an ideal gas at 25°c. 1. an isothermal expansion from 1 l to 10 l at an external pressure of 2.5 atm. 2. a free isothermal expansion from 1 l to 100 l. 3. a reversible isothermal expansion from 0.5 l to 4 l. 4. a reversible isothermal expansion from 0.5 l to 40 l. 5. an isothermal expansion from 1 l to 100 l at an external pressure of 0.5 atm.

Answer : The order of process from (1) the least work done by the system to (5) the most work done by the system will be:

(1) < (5) < (3) < (4) < (2)

Explanation :

The formula used for isothermally irreversible expansion is :

where,

w = work done

= external pressure

= initial volume of gas

= final volume of gas

The expression used for work done in reversible isothermal expansion will be,

where,

w = work done = ?

n = number of moles of gas = 1 mole

R = gas constant = 8.314 J/mole K

T = temperature of gas =

= initial volume of gas

= final volume of gas

First we have to determine the work done for the following process.

(1) An isothermal expansion from 1 L to 10 L at an external pressure of 2.5 atm.

(2) A free isothermal expansion from 1 L to 100 L.

(3) A reversible isothermal expansion from 0.5 L to 4 L.

(4) A reversible isothermal expansion from 0.5 L to 40 L.

(5) An isothermal expansion from 1 L to 100 L at an external pressure of 0.5 atm.

Thus, the order of process from (1) the least work done by the system to (5) the most work done by the system will be:

(1) < (5) < (3) < (4) < (2)

< > according to newton's third law of motion, forces always act in equal but opposite pairs. another way of saying this is for every action, there is an equal but opposite reaction.< >

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