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,

Question

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,, the graph is a straight line parallel to the time axis, the heat capacity of the liquid is inversely proportional to the slope of the graph, if some heat were lost at a constant rate to the surroundings during heating, the graph would be a straight line but with a larger slope, the internal energy of the liquid increases quadratically with time

MARKS App · Accepted Answer

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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