A liquid takes 5 minutes to cool from 80°C to 50°C. How much time (in min.) will it take to cool from 60°C to 30°C? The temperature of surrounding is 20°C. Use exact method.
Physics · Thermodynamics
JEE Advanced

Question

A liquid takes 5 minutes to cool from 80°C to 50°C. How much time (in min.) will it take to cool from 60°C to 30°C? The temperature of surrounding is 20°C. Use exact method.

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.