JEE Main & Advanced Physics Transmission of Heat Question Bank Topic Test - Transmission of Heat (3-5-21)

A body takes 5 minute to cool from \[80{}^\circ C\] to \[50{}^\circ C\]. How much time it will take to cool from \[60{}^\circ C\] to \[30{}^\circ C\], if room temperature is \[20{}^\circ C\].

A) 40 minute

B) 9 minute

C) 30 minute

D) 20 minute

Correct Answer: B

Solution :

According to Newtons law of cooling

in first case,\[\frac{80-50}{5}=K\left[ \frac{80+50}{2}-20 \right]\] ..(i)

in second case,\[\frac{60-30}{t}=k\left[ \frac{60+30}{2}-20 \right]\] (ii)

Dividing equation (i) by (ii) we get, \[\frac{t}{2}=\frac{45}{25}\]\[\Rightarrow \]\[t=9\]min.