Question

A body takes T minutes to cool from ${62}^{\circ }$ C to${61}^{\circ }$ C when the surrounding temperature is ${30}^{\circ }$ C .The time taken by the body to cool from ${46}^{\circ }$ C to ${45.5}^{\circ }$ C is

• A. Greater than T minutes
• B. Equal to T minutes
• C. Less than T minutes
• D. Equal to T/2 minutes

Answer 1

The correct option is B Equal to T minutes

In first step
$\frac{62-61}{T}=K[\frac{62+61}{2}-{30}^{\circ }]\Rightarrow \frac{1}{T}=K\left[31.5\right]$ ....(i)
In second step, suppose process takes T min then
$\frac{46-45.5}{T^{{}^{\prime }}}=K[\frac{46+45.5}{2}-30]\frac{0.5}{T^{{}^{\prime }}}=K\left[15.75\right]$ ...(ii)
On diving equation (i) and (ii) $\frac{2T^{{}^{\prime }}}{T}=2\Rightarrow T^{{}^{\prime }}=T$