KVPY 2019 SB SX Exam Previous Papers

Question : 33 of 120

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A heater supplying constant power P watts is switched on at time t = 0 minutes 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 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 of 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.

Validate

Solution:

P = \ms{\dT}/{\dt}

⇒

∫↖{1}↙{0}\Pdt=∫↖{T}↙{T_0}\msdT

= Pt = \ms (T -T_0)

⇒

T =P/{\ms}t+T_0

where

T_0

is temperature at

t = t_0

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