Suppose 0.550 mol of an ideal gas is isothermally and...

Suppose $0.550 \mathrm{~mol}$ of an ideal gas is isothermally and reversibly expanded in the four situations given below. What is the change in the entropy of the gas for each situation? $$\begin{array}{lcccc}\hline \text { Situation } & (\mathrm{a}) & (\mathrm{b}) & (\mathrm{c}) & (\mathrm{d}) \\\hline \text { Temperature }(\mathrm{K}) & 250 & 350 & 400 & 450 \\\text { Initial volume }\left(\mathrm{cm}^{3}\right) & 0.200 & 0.200 & 0.300 & 0.300 \\\text { Final volume }\left(\mathrm{cm}^{3}\right) & 0.800 & 0.800 & 1.20 & 1.20 \\\hline\end{array}$$

Key Concepts

Logarithmic Relationship in Entropy Change

The formula ?S = nR ln(V_f/V_i) reflects the logarithmic dependency of the change in entropy on the volume ratio. This logarithmic term arises from integrating the differential heat transfer over the process and emphasizes that the increase or decrease in entropy depends on how much the volume is expanded or compressed, regardless of the constant temperature.

Ideal Gas Behavior

Ideal gases follow the ideal gas law (PV = nRT), which relates pressure, volume, and temperature. This relationship simplifies the analysis of thermodynamic processes involving ideal gases, such as calculating work, heat transfer, and entropy changes in isothermal processes.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout. For an ideal gas undergoing such a process, the internal energy does not change, so any work done by or on the system is exactly compensated by heat flow, keeping the temperature constant.

Entropy Change in Reversible Processes

Entropy is a state function that measures disorder. In a reversible process, the change in entropy is given by the integral of the reversible heat transfer divided by the temperature, ?S = ?(?q_rev)/T. For an isothermal process involving an ideal gas, this leads to the expression ?S = nR ln(V_f/V_i), where n is the number of moles, R is the universal gas constant, and V_f and V_i are the final and initial volumes, respectively.

Transcript

Please give Ace some feedback