One mole of an ideal gas is isothermally expanded from 5.0 L to 10.0 L at 300 K. Compute the entropy changes for the system, surroundings, and the universe if the process is carried out (a) reversibly by adjusting the pressure of the surroundings to match the internal pressure of the gas, and (b) irreversibly, freely expanding in a vacuum.

Explanation:

(a)  Formula for work done in isothermal process is as follows.

                    =

                    = -1729 J

And, for isothermal process

                    =

According to the first law of thermodynamics,

Hence, = 1729 J

Also,  

                         =

                         = 5.763 J/K

Here,   = -1729 J

So,

        =

                 = 5.763 J/K -

Hence, entropy changes for reversibly by adjusting the pressure of the surroundings to match the internal pressure of the gas is 5.763 J/K - .

(b)  Now, formula for work done in irreversible isothermal process is as follows.

              W =

                   =

                   = -1000 J

For isothermal irreversible process,

            = 0

And,     = -W + 1000 J

                      =

                      = 3.33 J/K

    = -1000 J

Therefore,  

As,  

                     =

Hence, for irreversibly entropy changes freely expanding in a vacuum is .

no, the red giant is the hottest with 2.00.000.000 degrees celsius. while the white dwarf only 25,000 degrees celsius.