KCET 2018 Physics Solved Paper

Given, cup of tea cools from 65.5 °C to 62.5 °C in 1 minute.
Room temperature = 22.5 °C
We know that ‌

dT

dt

=k(θ−θ0) → (1)
For 1st case :‌

dT

dt

=‌

65.5−62.5

1min

=‌

3∘C

1

Also,θ−θ0=41.5∘C
Now, substituting in Eq. (1), we get
3=k(41.5)
⇒k=

3

41.5

→ (2)
For 2nd case : ‌

dT

dt

=‌

46.5−40.5

t

=‌

6∘C

t

Also, ⇒θ−θ0=21∘C
Again, substituting in Eq. (1), we get
‌

6

t

=k×21
Substitute value of k from Eq. (2), we get
‌

6

t

=‌

3

41.5

×21
⇒t=‌

6×41.5

3×21

=3.9523
⇒t~4 minutes