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A cylindrical block of length 0.4 m and cross-sectional area 0.04 m² sits coaxially on a thin metal disc of mass 0.4 kg with the same cross-section. The top face of the cylinder is held at 400 K while the disc starts at 300 K. The cylinder's thermal conductivity is 10 W/m-K and the disc's specific heat is 600 J/kg-K. Treating the disc's conductivity as very high and the system as insulated except at the top face, how long does the disc take to warm to 350 K?

1. 166 s
2. 120 s
3. 240 s
4. 83 s

Correct answer: 166 s

Solution

The energy balance reduces to (400 - T) = 240 dT/dt, whose integral from 300 to 350 K gives t = 240 ln 2 which is about 166 s.

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