A cubical tank of water of volume 1 m³ is kept at a constant temperature of 65°C by 1 KW heater. At time t = 0 , the heater is switched off. Find the time taken for the tank to cool down to 50°C, give

Question

A cubical tank of water of volume 1 m³ is kept at a constant temperature of 65°C by 1 KW heater. At time t = 0 , the heater is switched off. Find the time taken for the tank to cool down to 50°C, given the temperature of the room is steady at 15°C. Density of water = 1 0 3 kg m⁻³ and specific heat = 1.0 cal g⁻¹ °C⁻¹. (Do not assume average temperature during cooling). Take 1 KW = 240 cal s⁻¹.

TestHub · Accepted Answer

Steady state: 240 = k ( 65 − 15 ) , so k = 4.8 cal s⁻¹ °C⁻¹. C = 1 0 6 cal/°C. C d t d θ ​ = − k θ (with θ the excess over the room) gives t = k C ​ ln 35 50 ​ = 2.083 × 1 0 5 × 0.3567 = 74307 s = 20.64 h.

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