Question

drive an expression describes the change in entropy by an isobaric thermodynamics process in term of the initial and final voumes of the ideal gas

Answer 1

Answer on Question #43121-Physics-Molecular Physics-Thermodynamics

Derive an expression describes the change in entropy by an isobaric thermodynamics process in term of the initial and final volumes of the ideal gas

Solution

In the isobaric process of an ideal gas, the infinitesimal amount of heat is given by

$$\delta Q = d U + p d V = C _ {V} d T + p d V.$$

From the equation of state of the ideal gas

$$p V = n R T$$

follows

$$T = \frac {p V}{n R}, d T = \frac {p d V}{n R}.$$

Substituting this into

$$d S = \frac {\delta Q}{T},$$

one obtains

$$d S = \frac {C _ {V} \frac {p d V}{n R} + p d V}{\frac {p V}{n R}} = (C _ {V} + n R) \frac {d V}{V} = C _ {P} \frac {d V}{V}.$$

The change in entropy is given by

$$\Delta S = \int_ {V _ {i}} ^ {V _ {f}} C _ {P} \frac {d V}{V} = C _ {P} \ln \left(\frac {V _ {f}}{V _ {i}}\right),$$

where $V_{f}$ is the final volume of the ideal gas, $V_{i}$ is the initial volume of the ideal gas, $C_{P}$ is the heat capacity of the ideal gas at constant pressure.

http://www.AssignmentExpert.com/