Two identical samples of an ideal gas undergo separate isothermal expansions at 298 K

CHEMISTRY · Single correct · A Level · Chemistry · Thermodynamics · Thermodynamics

Problem

Two identical samples of an ideal gas undergo separate isothermal expansions at 298 K. • Sample I: expands from 2.0 L to 6.0 L. • Sample II: expands from 1.0 L to 4.0 L. Which of the following statements is most accurate about the magnitude of the entropy change for each sample? (a) Sample I experiences the greater increase in entropy because its absolute volume increase (ΔV=4 L) is larger than that of Sample II.\text{Sample I experiences the greater increase in entropy because its absolute volume increase }(\Delta V = 4\,\text{L})\text{ is larger than that of Sample II.} (b) Both samples experience the same entropy change because the temperature is identical for both expansions.\text{Both samples experience the same entropy change because the temperature is identical for both expansions.} (c) Sample II experiences the greater increase in entropy because its volume change represents a larger multiplying factor (Vf/Vi).\text{Sample II experiences the greater increase in entropy because its volume change represents a larger multiplying factor }(V_f/V_i). (d) Sample II experiences the smaller increase in entropy because ln⁡(Vi/Vf) is more negative for its expansion.\text{Sample II experiences the smaller increase in entropy because }\ln(V_i/V_f)\text{ is more negative for its expansion.}

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