Question

Calculate the entropy change when a He atom in the gas phase expands from V1 to 2V1 at constant temperature.

A) 5.8 kJ/K

B) 9.6 x 10-24 kJ/K

C) -5.8 kJ/K

D) 0 kJ/K

E) not enough information

Answer 1

Answer, -

.............b ) 9.6 x 10^-24

Explanation -

Since the heat (q ) has a randomising influence on the system , change in entropy S is related with q .

The heat ( q ) also depends on the temperature . Accordingly, the change in entropy, is mathematically calculated as

S₂ - S₁   = S = ( q_2(rev) / T - q_1(rev) / T ]

Even though the system is at constant temperature , but expansion of the gas involves a heat change at constant temperature . The heat change during the process is , therefore needed to calculate the exact value of S

Again ,

(i)entropy change is proportional to heat change due to expansion of a gaseous system the change in entropy is calculated as follows-

(ii) according to the problem the entropy change of a atom when the volume of the gaseous system changes from initial volume V1 to a final volume V2 is required to be calculated , the following expression should be used,

S= 2.303 nR log V_f / V_i

given V_f = 2 V1 & V_i = V1 ,

therefore for one mole (ie. n =1 )

S = 2.303 x 1 x 8.3145 log (2 V1 / V1 )

& for a atom          S = ( 2.303 x 8.3145 log 2.0 ) / 6.022 x 10²³

.........................................= 9.6 x 10^-24