A pan filled with hot food cools from 50.1 °C to 49.9 °C in 5 sec. How long (in sec.) will it take to cool from 40.1°C to 39.9°C if room temperature is 30°C ?
Physics · Thermodynamics
JEE Mains

Question

A pan filled with hot food cools from 50.1 °C to 49.9 °C in 5 sec. How long (in sec.) will it take to cool from 40.1°C to 39.9°C if room temperature is 30°C ?

G1 Physics · Accepted Answer

Use the first law Q=ΔU+W (W by the gas), ΔU=nCᵥΔT for an ideal gas, and the appropriate process relation. For Carnot devices, let T₁ be the cold-reservoir temperature and T₂ be the hot-reservoir temperature; η=1−T₁/T₂ and COP=T₁/(T₂−T₁). Substituting the given values gives 10.