JEE Main20236 Apr 2023Evening ShiftPhysicsThermal Properties of MatterActual
A body cools in 7 minutes from 60 o C to 40 o C . The temperature of the surrounding is 10 o C . The temperature of the body after the next 7 minutes will be
Options
- A30 o C
- B32 o C
- C34 o C
- D28 o C
Correct answer
D. 28 o C
Step-by-step solution
Newton's law of cooling states that T 1 - T 2 t = K T 1 + T 2 2 - T 0       . . . ( i ) where T 0 is the temperature of the surrounding. From equation (i), 60 - 40 7 × 60 = K 60 + 40 2 - 10 ⇒ 20 7 × 60 = 40 K ⇒ K = 20 7 × 60 × 40 Let the temperature of the body after the given time be x   ° C . By Newton's law of cooling, 40 - x 7 × 60 = K 40 + x 2 - 10 ⇒ 40 - x 7 × 60 = 1 14 × 60 ( 20 + x 2 ) ⇒ 160 - 4 x = 20 + x ⇒ x