IGNOU BMTC 132 2026 - Suppose that a thermometer having a reading of inside a hou

Question

Suppose that a thermometer having a reading of $75^\circ\text{F}$ inside a house is placed outside where the air temperature is $15^\circ\text{F}$ . Two minutes later it is found that the thermometer reading is $30^\circ\text{F}$ . Find the temperature reading T(t) of the thermometer at any time t.

09 Jan 2026

Answer :

Word Count : 183

The problem is an application of Newton's Law of Cooling, which states: [ \frac{dT}{dt} = -k(T - T_{\text{env}}) ] where (T(t)) is the temperature of the object, (T_{\text{env}}) is the surrounding temperature, and (k > 0) is a constant. Here: [ T_{\text{env}} = 15^\circ F, \quad T(0) = 75^\circ F, \quad T(2) = 30^\circ F ] The general solution of Newton's law is: [ T(t) = T_{\text{env}} + (T_0 -

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