Question

In further 10 minutes it will cool from ${38}^{\circ }$ to

• A. ${36}^{\circ }$
• B. ${36.4}^{\circ }$
• C. ${37}^{\circ }$
• D. ${37.5}^{\circ }$

Answer 1

The correct option is B ${36.4}^{\circ }$

$Wehave\theta -{\theta }_s=({\theta }_0-{\theta }_s)e^{-kt}.....\left(1\right)Where=initialtemperatureofbody=40℃\theta =temperatureofbodyaftertimet{\theta }_s=temperatureofsurroundingSincebodycoolsfrom40℃to38℃in10min,wehave38-30=(40-30)e^{-10k}....\left(2\right)Letafter10min,thebodytempbe\theta ,\theta -30=(38-30)e^{-10k}.....\left(3\right)Dividingeq\left(2\right)byeq\left(3\right)gives\frac{8}{\theta -30}=\frac{10}{8}\Rightarrow \theta -30=6.4\Rightarrow \theta ={36.4}^o$