Show that during the quasistatic isothermal expansion of a monatomic ideal gas, the change in entropy is related to the heat input Q by the simple formula

In the following chapter I’ll prove that this formula is valid for any quasistatic process. Show, however, that it is not valid for the free expansion process described above.

Step 1 of 5</p>

For a quasistatic isothermal process,differential work done is equal to the product of pressure and change in volume and is given by,

Since it is isothermal process, temperature remains constant.

For such a process, the heat absorbed or emitted is given by,

Where is change in internal energy.

Using

………...1

Step 2 of 5</p>The Sackur Tetrode equation gives the entropy of a monatomic gas molecule as,

……….2

Where S is entory, N is avogadro number, k and h are constants, m is mass of argon atom, V is volume and U is internal energy.

Step 3 of 5</p>

The change in entropy will be due to combined effects of change in volume and internal energy.

That is,

Using equation 2,

On differentiating,