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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A hot liquid is placed in a large room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted as a function of time. The resulting plot will be very nearly

Options

  1. Aa parabola
  2. Ba circular arc
  3. Ca straight line
  4. Dan ellipse

Correct answer

C. a straight line

Step-by-step solution

According to Newton's law of cooling, the rate of change of temperature is proportional to the temperature difference between the object and its surroundings. dT dt = -k(T - T₀) Let T = T - T₀ be the temperature difference. d( T) dt = -k T Integrating both sides: d( T) T = -k dt ( T) = -kt + C This equation is of the form y = mx + c , where y = ( T) and x = t . Thus, the plot of the logarithm of the temperature difference versus time is a straight line with a negative slope.

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