CASE STUDY CHALLENGE
Newton’s Law of Cooling: Laptop Processor
During a heavy gaming session, the temperature of a laptop processor increases significantly. After the session, it cools at a rate proportional to the difference between the processor’s temperature and the room temperature (25°C).
Initially, the processor’s temperature is 85°C. The rate of cooling is defined by the differential equation:
\[ \frac{d}{dt} T(t) = -k(T(t) – 25) \]
Where \( T(t) \) is the temperature at time \( t \) and \( k \) is a constant.
Answer the following:
| (i) | Find the expression for \( T(t) \), given that \( T(0) = 85^\circ \)C. | [2 Marks] |
| (ii) | How long will it take for the temperature to reach \( 40^\circ \)C? (Given \( k = 0.03 \), \( \log_{e} 4 = 1.3863 \)). | [2 Marks] |