A gas expands from state i to state f in the figure, with the pressure remaining constant. Which equation best describes the relationship between the initial and final volumes and temperatures according to the ideal gas law?

• A. V_i T_i = V_f T_f
• B. P_i / T_i = P_f / T_f
• C. V_i / T_i = V_f / T_f
• D. P_i V_i = P_f V_f

Answer: (C)

Verified step by step guidance

1. Identify the given conditions: the gas expands at constant pressure, meaning \(P_i = P_f\).
2. Recall the ideal gas law: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles of gas, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
3. Since pressure and the amount of gas (\(n\)) remain constant, rearrange the ideal gas law to relate volume and temperature: \(V \propto T\) at constant \(P\).
4. Express this proportionality as an equation relating initial and final states: \(\frac{V_i}{T_i} = \frac{V_f}{T_f}\).
5. This equation shows that the ratio of volume to temperature remains constant during the expansion at constant pressure.