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 ?
BITSAT
Physics
Thermal Properties of Matter
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Physics Question (2023) — Solution
Options
- A. 2 minutes
- B. 1.4 minutes
- C. 0.5 minute
- D. 1 minute
Answer
B. 1.4 minutes
Step-by-step solution
The rate of heat flow is given by aligned & Q t =-K (T-T_0 ) Q t =-K (T_ a v g -T_0 ) \\ & Initially T_ a v g = T_1+T_2 2 \\ & Here, T_1=98^ C \\ & T_2=86^ C aligned aligned & (i) ms 12 2 =- K ( 98+86 2 -22 ) \\ & 6=- K ms [ 98+86 2 -22 ] ( Q = ms T ) aligned Now, cool from T _1^ =75^ C aligned & T _2=69^ C \\ & T _ avg = T _1^ + T _2^ 2 = 75+69 2 aligned (ii) ms 6 t =- K ( 75+69 2 -22 ) Divide equation (ii) by (i), we have aligned & 6 t(6) = 50 70 \\ & t= 7 5 =1.4 ~min aligned
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