A real gas obeys the equation P ( V m − b ) = RT , where ( b = 0.1 L / mol ) , if 2 moles of gas is slowly compressed from 1.2 litre to 0.6 litre at 300 K, then calculate the work done (in kJ ) on t

Question

A real gas obeys the equation P ( V m ​ − b ) = RT , where ( b = 0.1 L / mol ) , if 2 moles of gas is slowly compressed from 1.2 litre to 0.6 litre at 300 K, then calculate the work done (in kJ ) on the gas, in the process. [Given : ln2 = 0.7, ln5 = 1.6, R = 8.314 J/K-mol]

TestHub · Accepted Answer

Formula: For a real gas obeying P ( V − nb ) = n RT , the work done on the gas during isothermal compression is W = n RT ln ( V 2 ​ − nb V 1 ​ − nb ​ ) . Given Data: n = 2 m o l , T = 300 K , b = 0.1 L / m o l ⟹ nb = 0.2 L , V 1 ​ = 1.2 L , and V 2 ​ = 0.6 L . Substitution: W = 2 × 8.314 × 300 × ln ( 0.6 − 0.2 1.2 − 0.2 ​ ) = 600 × 8.314 × ln ( 2.5 ) . Log Calculation: Using the given values, ln ( 2.5 ) = ln ( 5 ) − ln ( 2 ) = 1.6 − 0.7 = 0.9 . Final Answer: W = 600 × 8.314 × 0.9 = 4489.56 J ≈ 4.49kJ .

Chemistry - Thermodynamics - I Question with Solution | TestHub

Doubts & Discussion