Answer to Question #125655 in Electric Circuits for Vidurjah Perananthan

Question

In an attempt to determine the effect of a stove, Pelle heated 0.8 liters of water in a saucepan. To raise the pot temperature by 1 K, the energy 50 J needs to be supplied.
The saucepan was then placed on a stove plate which was screwed up to full power.
He measured the temperature as a function of time and got the following results - see diagram below.
a) Explain the appearance of the diagram
b) Use measurement data and your formula collection to determine the effect of the cooker plate
c) Describe the simplifications you have made

Answer 1

a)    As we see in the diagram, the temperature increases with time according to a nonlinear law. The part between the initial temperature and 100°C looks linear, at the level of 100°C the temperature stopped increasing because of the boiling processes: evaporation occurs with no temperature increase.

b)    To determine the efficiency of the cooker plate, we need to divide the output energy by the energy required to heat the water till its boiling point. We need to measure the voltage and current of the stove plate and time required to increase the temperature to 100°C.

Since we have no images here, assume that the stove was functioning at a standard voltage of 120 V, the current was 1 A, the elapsed time was 1 min, and the initial temperature of water was 20 degrees. The energy "output" is equal to the thermal energy of water:

$$Q_o=k\Delta t=50\text{ J/°C}\cdot(100°\text{C}-20°\text{C})=4000\text{ J}.$$

The energy "input" was

$$Q_i=Pt=VIt=1200\cdot1\cdot60=7200\text{ J}.$$

The efficiency is

$$\eta=\frac{Q_o}{Q_i}\cdot100\%=56\%.$$

c) We have made the following simplification: assumed that the current was constant all the time (it is not true because due to temperature increase the resistance increases, making current decrease).