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KVPY2019PhysicsThermal Properties of Matter

A heater supplying constant power P watts is switched ON at time t = 0   min to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. A student records the temperature of the liquid T t at equal time intervals. A graph is plotted with T t on the Y -axis versus t on the X -axis. Assume that there is no heat loss to the surroundings during heating. Then,

Options

  1. Athe graph is a straight line parallel to the time axis
  2. Bthe heat capacity of the liquid is inversely proportional to the slope of the graph
  3. Cif some heat were lost at a constant rate to the surroundings during heating, the graph would be a straight li
  4. Dthe internal energy of the liquid increases quadratically with time

Correct answer

B. the heat capacity of the liquid is inversely proportional to the slope of the graph

Step-by-step solution

Assuming no heat loss, Heat gained by liquid in calorimeter = Heat supplied by heater ⇒ m S T f - T i = P t ⇒ T f = P m S t + T i Comparing above equation with y = m x + c , S!ope of line = P m S or slope ∝ 1 S So, graph of T versus t is as shown below.

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