A bowl filled with very hot soup cools from 98°C to 86^° C in 2 minutes when the room temperature is 22^° C . How long it will take to cool from 75^°…

Question

A bowl filled with very hot soup cools from 98°C to 86^° C in 2 minutes when the room temperature is 22^° C . How long it will take to cool from 75^° C to 69^° C ?

MARKS Content Team · Accepted Answer

Correct answer: (B) 1.4 minute. From Newton's law of cooling, we have (ΔQ)/(Δt)=-KT_avg-T_0 Where, Q=ms∆T, m is the mass, s is the specific heat and ∆T is the temperature change. Case 1: ∆t=2 minutes, T_0=22°C (ms×12)/2=-K(98+86)/2-22 6=-K/ms70 ...1 Case 2: (ms×6)/(Δt)=-K(75+69)/2-22 6/(Δt)=-K/ms(50) ...2 Dividing (2) by (1), we get ⇒6/(Δt(6))=50/70 ⇒Δt=7/5=1.4 min

A bowl filled with very hot soup cools from $98 ° C$ to $86^{\circ} \mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ} \mathrm{C}$. How long it will take to cool from $75^{\circ} \mathrm{C}$ to $69^{\circ} \mathrm{C}$ ?

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Relevant Questions

A bowl filled with very hot soup cools from 98°C to $86^{\circ} \mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ} \mathrm{C}$. How long it will take to cool from $75^{\circ} \mathrm{C}$ to $69^{\circ} \mathrm{C}$ ?

Solution

Relevant Questions

A bowl filled with very hot soup cools from $98 ° C$ to $86^{\circ} \mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ} \mathrm{C}$. How long it will take to cool from $75^{\circ} \mathrm{C}$ to $69^{\circ} \mathrm{C}$ ?