Engineering
Physics
Radiation
Question

Two identical beakers A and B contain equal volumes of two different liquids at 60º C each and left to cool down. Liquid in A has density 8 × 102 kg/m3 and specific heat of 2000 J kg–1 K–1 while liquid in B has density of 103 kg m–3 and specific heat of 4000 J kg–1 K–1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

 

 

 

 

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Solution

−msdTdt=eσA(T4−T04)

−dTdt=eσAms(T4−T04);dTdt=4eσAT03ms(ΔT)

T = T0 + (Ti – T0)e-kt

where  k=4eσAT03ms

k=4eσAT03ρvs;|dTdt|∝k

∴    |dTdt|∝1ρs

ρASA = 2000 × 8 × 102 = 16 × 105

ρBSB = 4000 × 103 = 4 × 106

ρASA < ρBSB

|dTdt|A>|dTdt|B