UPSC Combined Geo-Scientist, Mains · 2019 · Mains Paper II
Q1(a). Atomicity from heat capacities
Question
The ratio of the estimated constant-volume molar heat capacity of a linear N-atomic molecule to its nonlinear counterpart, using equipartition, is 13/12. Find N.
Answer in brief
N=3, in the fully excited classical limit.
Key points
- Translation contributes 3R/2 for either geometry. Linear rotation contributes R; nonlinear rotation contributes 3R/2.
- Each vibration contributes R when fully excited. The vibration counts are 3N-5 and 3N-6, respectively, so C_(V,m)lin=(3N-5/2)R and C_(V,m)nonlin=(3N-3)R.
- Thus (3N-5/2)/(3N-3)=13/12. Cross-multiplication gives 36N-30=39N-39, hence N=3. The heat capacities are then 13R/2 and 6R.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversAtomicity from heat capacitiesEquipartition
All parts of Question 1
- 1(a) Atomicity from heat capacities5 marks
- 1(b) Units of attraction parameter5 marks
- 1(c) Surface energy of cube and sphere5 marks
- 1(d) Atoms in a BCC sample5 marks
- 1(e) Volume independence of ideal-gas heat capacity5 marks
- 1(f) Entropy on doubling volume5 marks
- 1(g) Single-ion activity coefficients5 marks
- 1(h) Ammonia buffer5 marks
- 1(i) Pure-component vapour pressures5 marks
- 1(j) Zero-order half-life5 marks
- 1(k) Physical and chemical adsorption5 marks
- 1(l) Iron redox-electrode potential5 marks
- 1(m) Energy of one einstein5 marks
- 1(n) Bohr quantisation from matter waves5 marks
- 1(o) Spectral wavelength shifts5 marks
- 1(p) Bromobutane with one NMR signal5 marks