Question

please answer this......

Answer 1

Answer:

the correct answer is 4min.......◉‿◉

Explanation:

see the pics I hope uh understand properly(•‿•)

Answer 2

Given :-

• A cup of tea cools from 65.5° C to 62.5° in 1 minute.
• Room temperature = 22.5°C

To Find :-

• Time taken it take to cool from 46.5°C to 40.5°C.

$\begin{gathered}\Large{\bold{\pink{\underline{CaLcUlAtIoN\::}}}} \end{gathered}$

Using Newtows Law of Cooling

$\bf \: ⟼ \dfrac{dθ}{dt} = k(θ - θ_0)$

where,

$\bf \: ⟼ θ_0 = 22.5$

$\bf \: ⟼ θ = \dfrac{65.5 + 62.5}{2} = 64$

$\bf \: ⟼ \dfrac{dθ}{dt} = \dfrac{65.5 - 62.5}{1} = 3$

$\begin{gathered}\bf\red{So,}\end{gathered}$

$\bf \: ⟼ 3 = k(64 - 22.5)$

$\bf \: ⟼ k = \dfrac{3}{41.5} \: ⟼ \: (1)$

Again, now

Let time taken be 't' minutes.

$\bf \: ⟼ \dfrac{dθ}{dt} = k(θ - θ_0)$

where,

$\bf \: ⟼ θ = \dfrac{46.5 + 40.5}{2} = 43.5$

$\bf \: ⟼ \dfrac{dθ}{dt} = \dfrac{46.5 - 40.5}{t} = \dfrac{6}{t}$

$\begin{gathered}\bf\red{So,}\end{gathered}$

$\bf \: ⟼ \dfrac{6}{t} = \dfrac{3}{41.5} \times (43.5 - 22.5)$

$\bf \: ⟼ \dfrac{6}{t} = \dfrac{3}{41.5} \times 21$

$\bf \: ⟼ t = \dfrac{83}{21}$

$\bf \: ⟼ t = 4 \: minutes \: (approx)$