# Determine thermodynamics quantities with 1 data

1. Apr 24, 2009

### Goddar

1. The problem statement, all variables and given/known data
Each molecule of a certain substance can exist in either of two states; these states differ in energy by 25 eV.

a. If one mole is in equilibrium at room temperature, what is the fraction of atoms in the excited state?

b. What is the entropy of this sample at room temperature?

c. What is the internal energy of this sample at room temperature?

d. What is the free energy F of this sample at room temperature?

2. Relevant equations
see below

3. The attempt at a solution
a. seems easy, using Boltzmann's factors (T = 298K); i get exp(–974), which is essentially 0 for all practical purposes: no atom in the excited state.

b.c.d. i can't get around these with the information given: i would need at least the value of the ground state energy to use:
U = NAE0, avogadro's number times ground energy
F = –NAkT*lnZ, where Z is the sum of Boltzmann's factors
S = –NA(dF/dT)

Am I missing something really obvious, here?..