Q. 9

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 arc

C. a parabola

D. an ellipse

Answer :

When a hot liquid is kept in a big room, the temperature of the hot liquid will decrease with time. The room is big hence the difference between emitted radiation and absorbed radiation by the walls would be large. According to Stefan’s Law, the energy of thermal radiation emitted per unit time is directly proportional to T4. The Temperature would show an exponentially decreasing behavior against time. After a sometime, temperature of the liquid becomes equal to the temperature of the surrounding resulting in zero temperature difference. When logarithm of temperature difference is taken, the fourth power becomes coefficient as per the logarithmic properties,

Here T is the emitted radiation and T0 is the absorbed radiation. Thus, the logarithmic plot would be a straight line as logarithmic graphs are nonlinear variables converted to linear graphs.
Thus, option (a) is the correct option.

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