Please help me, I'm on my last attempt!
Calculate the change in entropy when the pressure of 5.75 g of helium gas is decreased from 320.0 kPa to 40.0 kPa while the temperature decreases from 423 K to 273 K. Assume ideal behavior.
- az_lenderLv 71 month ago
Since entropy is a state variable, the entropy change may be path-independent so long as the process is quasi-static.
So let's say you first decrease the pressure by a factor of 8 without changing T, but then reduce the temperature without changing V or p.
During that first process, the gas will do work and must therefore absorb heat to achieve its expansion (as temperature is not changing). The work done is the integral of p delta-v
= RT ln(p1/p2)
= (8.314 J/molK)(423 K) ln(8)
Therefore, the gas must absorb 7.313 kJ/mol of heat during this first process, and as this heat is all absorbed at 423K, the entropy change is Q/T = 17.288 J/(mol K).
But now the gas is cooled at constant pressure to 273 K. For a monatomic gas (helium), the molar specific heat is (5/2)R
= 20.785 J/(molK). To find the entropy change, we integrate
dQ/T = (20.785 J/(molK))* dT/T
= (20.785 J/molK)*ln(273/423) = -9.102 J/molK.
So the overall entropy change is +8.2 J/molK, arising mainly from the injection of heat needed to achieve the volume increase.