A cup of tea is cooled in a room whose constant temperature is

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

25^{\circ}\text{C}

. The temperature of the tea is

90^{\circ}\text{C}

t=0

minutes and

60^{\circ}\text{C}

after

10

minutes. (i) Formulate the differential equation that models the temperature

T(t)

of the tea at time

t

minutes, clearly stating any assumptions. (ii) Solve the differential equation to obtain

T(t)

in terms of the ambient temperature and an arbitrary constant. (iii) Using the numerical data, determine the cooling constant

k

(correct to four decimal places). (iv) Predict the temperature of the tea after

20

minutes. Give your answer correct to one decimal place.