Physics · Heat transfer: conduction, convection and radiation
A hot liquid is kept in a big room. The logarithm of the numerical value of the
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.
Step-by-step solution
Newton's law of cooling states that the rate of heat loss is proportional to the temperature difference. For a small difference, d(ΔT)/dt = -kΔT, leading to ΔT = ΔT₀ e^{-kt}. Taking logarithm gives ln(ΔT) = ln(ΔT₀) - kt, which is a linear equation in time. Thus a plot of ln(ΔT) versus time is a straight line.
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