Question

Use these steps to answer the questions below:

Step 1: A sample of monoatomic ideal gas, initially at pressure P₁ and volume V₁, expands isothermally and reversibly to a final pressure P₂ and volume V₂

Step 2: The ideal gas is compressed isothermally back to its initial conditions using constant pressure.

Give the equation needed to solve for the following

Wsys (Step 1) =

qsys (Step 2) =

Answer 1

Step -1

The following equation should be used to calculate work done during expansion of the ideal gas undergoing a isothermal reversible change-

w_sys  = - 2.303 n RT log ( V2 / V1 )

Again since P1 V1 = P2 V2

  V2 / V1 = P1 / P2

& w_sys = - 2.303 nRT log ( P1 / P2 )   

Step -2

It involves compression of the system , hence work is done on the system . So compression work of an ideal gas may be derived similarly and it has exactly the same value with the sign changed.

Thus isothermal w_sys would have a positive value & q_sys  would then be negative.