Question

The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.

Answer 1

Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.

Therefore when expressed mathematically, this is equivalent to:

dT = - k (T – Ts) dt

dT / (T – Ts) = - k dt

Integrating:

ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)

Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.

R = ˚F + 460

T1 = 200 + 460 = 660 R

Ts = 70 + 460 = 530 R

ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)

T2 = 569.16 R

T2 = 109 ºF

Answer: After 2 hours, it will be 109 ºF