One mole of an ideal monoatomic gas in heated by supplying 5 kJ heat from a reservoir maintained at 400 K from 300 K to 400 K . In the process, the volume of gas increased from one litre to 10 litre.

Question

One mole of an ideal monoatomic gas in heated by supplying 5 kJ heat from a reservoir maintained at 400 K from 300 K to 400 K . In the process, the volume of gas increased from one litre to 10 litre. Find ( Δ S ) total ​ in J K − 1 ⋅ mol − 1 associated with the process (Given ℓ n 3 4 ​ = 0.3 , ℓ n 10 = 2.3 , R = 8.3 J K − 1 m o l − 1 and ℓ n x = 2.3 ℓ lo g 10 ​ x )

TestHub · Accepted Answer

The change in entropy for the system is given by:

$(Δ S)_{sys t e m} = C_{v} ln \frac{T _{2}}{T _{1}} + R ln \frac{V _{2}}{V _{1}}$

The change in entropy for the surroundings is:

$(Δ S)_{s u rr} = \frac{- q}{400}$

The total change in entropy is calculated as:

$(Δ S)_{t o t a l} = \frac{- 5000}{400} + \frac{3}{2} ln \frac{400}{300} + 8.3 ln \frac{10}{1} = \frac{- 50}{4} + \frac{3}{2} \times 0.3 + 8.3 \times 2.3 = - 12.5 + 0.45 + 19.09 = 7.04$

Chemistry - Thermodynamics - II Question with Solution | TestHub

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