Question

In 5 minutes, a body cools from 75°C to 65°C at a room temperature of 25°C. The temperature of the body at the end of the next 5 minutes is ______°C.

Options

• 55

• 56

• 57

• 54

Answer 1

In 5 minutes, a body cools from 75°C to 65°C at a room temperature of 25°C. The temperature of the body at the end of the next 5 minutes is 57°C.

Explanation:

By Newton's law of cooling,

`(DeltaT)/(Deltat) = -C(T_{"avg"} - T_s)`

In the first 5 minutes time,

`(-10^circC)/(5 min) = -C(70^circC - 25^circC)`

⇒ C = `2/45` min^-1

In the next 5 minutes time,

`(T - 65)/(5 min) = -C((T + 65)/2 - 25) = -(2/45)((T + 15)/2)`

⇒ 9(T - 65) = -(T + 15)

⇒ 10T = 570

∴ T = 57°C