UPSC Combined Geo-Scientist, Mains · 2019 · Mains Paper II
Q1(f). Entropy on doubling volume
Question
Find the molar entropy change in SI units when the volume of any ideal gas doubles at constant temperature.
Answer in brief
ΔSₘ=Rln 2=5.763 J mol⁻¹ K⁻¹.
Key points
- Along an isothermal reversible reference path, dS=δ qᵣₑᵥ/T=p dV/T=nR dV/V.
- Integrating and dividing by n gives ΔSₘ=Rln (V₂/V₁)=8.314ln 2.
- The result is positive and independent of gas identity.
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.
CoversEntropy on doubling volumeThermodynamics
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