Chemistry - Thermodynamics - I Question with Solution | TestHub
Match the column (assume CV,m is independent of temperature)
Column I | Column II |
|---|---|
P) dU = n· CV,m· dT | i) Ideal gas |
Q) dU = n· CV,m· dT + n2a(dV)/(V2) | ii) van der Waals gas |
R) dU = n2a(dV)/(V2) | iii) van der Waals gas in isothermal process |
| iv) van der Waals gas in isochoric process |
Options:
Answer:
Solution:
For an ideal gas U depends only on T, so dU = nCV,mdT (i); the same reduced form results for a van der Waals gas at constant volume, where dV = 0 kills the attraction term (iv) — P matches i,iv. For a van der Waals gas (∂ U/∂ V)T = n2a/V2, giving the full expression dU = nCV,mdT + n2a dV/V2; formally it also covers the isothermal case (dT = 0) and the isochoric case (dV = 0) — Q matches ii,iii,iv. Setting dT = 0 leaves dU = n2a dV/V2, the isothermal van der Waals result — R matches iii.
