Question

A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly
(a) a straight line
(b) a circular are
(c) a parabola
(d) an ellipse

Answer 1

Answer:

d is the correct answer

Answer 2

The plot will be very nearly a straight line.

Explanation:

• Thermal energy emitted by liquid is gained by the walls of room

• According to Stefan’s law fourth power of temperature

• That is power radiated by a black body is directly proportional to $T^{4}$

At equilibrium temperature of liquid must be equal to temperature of room

                      $Tliquid = Troom$

take log function       $\log \left(T^{4}\right)$

                                  $=4 \log T$  (from logarithmic property)  

Differentiate with respect to t  

              $\mathrm{d}(4 \log \mathrm{T}) / \mathrm{dt}=4 \mathrm{dT} / \mathrm{T}$

As the curve varies linearly hence the answer is straight line.