Question

The Gibb’s free energy equation for a system undergoing phase transition is given by \( \Delta G = \Delta H - T\Delta S \), where \( \Delta G \) is the change in Gibb’s free energy, \( \Delta H \) is the change in enthalpy, \( \Delta S \) is the change in entropy and \( T \) is the temperature in Kelvin.
During melting transition, two systems A and B, show no difference in \( \Delta H \) but B exhibits 10% lower \( \Delta S \). The ratio of melting temperature of B to that of A (rounded off to 2 decimal places) is ________________.

Hint:

When comparing melting temperatures for phase transitions, the ratio of temperatures is the inverse ratio of entropy changes, provided enthalpy changes are the same.

Answer 1

Correct Answer: 1.1

We start with the Gibb’s free energy equation:
\[ \Delta G = \Delta H - T\Delta S \] Since \( \Delta G = 0 \) for the melting point, we have:
\[ 0 = \Delta H - T \Delta S \] Thus, the melting temperature \( T = \frac{\Delta H}{\Delta S} \).
For systems A and B, since \( \Delta H \) is the same, we use the ratio of \( \Delta S \) values. Since B has 10% lower \( \Delta S \) than A, we have:
\[ \frac{T_B}{T_A} = \frac{\Delta S_A}{\Delta S_B} = \frac{1}{1 - 0.10} = \frac{1}{0.90} = 1.1111 \] Therefore, the ratio of the melting temperatures is 1.11.
Final Answer: 1.11