A heater supplying constant power P watts is switched ON at time … - Vidyadip

MCQ

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,

A
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
C
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
D
the internal energy of the liquid increases quadratically with time

✓

Answer

Correct option: B.

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

b
$(b)$ Assuming no heat loss,

Heat gained by liquid in calorimeter $=$

Heat supplied by heater

$\Rightarrow m S\left(T_{f}-T_{i}\right)=P t$

$\Rightarrow \quad T_{f}=\frac{P}{m S} t+T_{i}$

Comparing above equation with

$y=m x+c,$

Slope of line $=\frac{P}{m S}$

or $\operatorname{slope} \propto \frac{1}{S}$

So, graph of $T$ versus $t$ is as shown below.

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