UPSC Civil Services (Mains), Chemistry optional · 2025 · Paper I
Q1(d). Heat conduction between two copper sheets through air
Question
Two sheets of copper of area 1.50 m² are separated by 10 cm. What is the rate of transfer of heat by conduction from the warm sheet (50 °C) to the cold sheet (−10 °C)? What is the rate of loss of heat? (Assume the space between the two sheets is filled with air.) Given: Coefficient of thermal conductivity of air = 2.4 × 10⁻² J s⁻¹ m⁻¹ K⁻¹.
Answer in brief
Rate of heat transfer = 21.6 J s⁻¹; the warm sheet loses heat at the same rate, 21.6 W.
Key points
- In the steady state the gradient across still air between two parallel sheets is uniform, so Fourier’s law applies: J = −κ dT/dz.
- Gradient: dT/dz = (−10 − 50) K / 0.10 m = −600 K m⁻¹.
- Flux J = (2.4 × 10⁻²)(600) = 14.4 J m⁻² s⁻¹; rate = JA = 14.4 × 1.50 = 21.6 J s⁻¹.
- No heat collects in the air, so the warm sheet loses exactly what the cold sheet gains; the figure is small because still air is a poor conductor.
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.
Coversthermal conductivityFourier's lawheat fluxtransport properties of gasestemperature gradient
All parts of Question 1
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- 1(b) Born–Haber cycle for NaCl at 298 K5 marks
- 1(c) Raising the conductivity of Ge and Si by trace elements5 marks
- 1(d) Heat conduction between two copper sheets through air5 marks
- 1(e) Superheating of liquids and the Kelvin equation5 marks
- 1(f) Ascending order of dipole moment: NH₃, NF₃, H₂O5 marks
- 1(g) Heat of combustion of naphthalene from bomb calorimetry5 marks
- 1(h) Sealed sample: ethane, neon or a mixture5 marks
- 1(i) Time to plate a gold layer5 marks
- 1(j) Maximum work of a steam turbine5 marks