KCET 2016 Physics Solved Paper

Given, food cools from 94 °C to 86 °C in 2 minutes; room temperature = 20 °C
Now, ‌

dT

dt

=k(θ−θ0)
For 1st case, ‌

dT

dt

=‌

94−86

2

=‌

8

2

=4∘
and (θ−θ0)=‌

(94+86)

2

−20∘=70∘
∴4=k to ⇒k=‌

4

70

For 2nd case, ‌

dT

dt

=‌

74−66

t

=‌

8

t

and θ−θ0=‌

(74+66)

2

−20=50∘
∴‌

8

t

=‌

4

70

×50
⇒t=‌

8×70

4×50

=2.8
Thus, food cools from 74 °C to 66 °C in 2.8 minutes