Eduprobe
Question:
Two identical breakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 10² kg/m³ and specific heat of 2000 J kg⁻¹K⁻¹; while liquid in B has density of 10³ kg m⁻³ and specific heat of 4000 J kg⁻¹K⁻¹. Which of the following best describes their temperature versus time graph schematically?
Solution:
Correct option is A.
-ms(dT/dt) = eσA(T⁴ - T₀⁴)
-dT/dt = eσA/ms(T⁴ - T₀⁴)
-dT/dt = 4eσAT₀³/ms(ΔT)
T = T₀ + (Tᵢ - T₀)e⁻ᵏᵗ
where k = 4eσAT₀³/ms
k = 4eσAT₀³/ρvs
|dT/dt| ∝ 1/ρs
ρsA = 2000 × 8 × 10² = 16 × 10⁵
ρsB = 4000 × 10³ = 4 × 10⁶
ρsA < ρsB
|dT/dt|A > |dT/dt|B.