Question

Hot water cools from $42 ^ { \circ } \mathrm { C }$ in the next 10 minutes. The temperature of the surrounding is

• A.
• B.
• C. $15 ^ { \circ } \mathrm { C }$
• D.

Answer 1

Answer: (B)

Answer 2

According to Newton's law of cooling

$\frac { \theta _ { 1 } - \theta _ { 2 } } { t } = K \left[ \frac { \theta _ { 1 } + \theta _ { 2 } } { 2 } - \theta _ { 0 } \right]$

In the first case,

$1 = K ( 55 - \theta )$ ….(i)

In the second case,

$\frac { ( 50 - 42 ) } { 10 } = K \left[ \frac { 50 + 42 } { 2 } - \theta _ { 0 } \right]$ $0.8 = K \left( 46 - \theta _ { 0 } \right)$ ….(ii)

Dividing (i) by (ii), we get

$\frac { 1 } { 0.8 } = \frac { 55 - \theta _ { 0 } } { 46 - \theta _ { 0 } }$

or $46 - \theta _ { 0 } = 44 - 0.8 \theta _ { 0 }$ ⇒