How Does an Immersion Heater Transfer Energy to a Liquid?

[UrbanXrisis]

An immersion heater of resistance R converts electrical energy into thermal energy that is transferred to the liquid in which the heater is immersed. If the current in the hearter is I, the thermal energy trasferred to the liquid in time t is?

1) IRt

2) I^2Rt

3) IR^2t

4) IRt^2

5) IR/t

The answer is #2 but I don't see how my book got that answer.

 

[Janitor]

The voltage drop across a resistance R when the current is I is given by V=IR.
Note that voltage has units of energy/charge. Multiply the voltage by current, which has units charge/time, and you get the rate at which heat is generated in the resister, I^2R, the units being energy/time. If the current is steady, the total energy changed to the form of heat will just be that rate, I^2R, times the amount of time that you let the process run, that is: I^2 Rt.

 

[Chen]

mgh also has units of energy, does that make it right as well?

Think of an electron as it goes through the resistor. Its speed doesn't change (since the current is constant) so what does change, and where is the heat coming from? Let's consider the energies of the electron - it has kinetic energy and electric potential energy. The former doesn't change, but the latter does. The 'lost' energy becomes heat:
ΔE_k + ΔE_p = ΔE_T
ΔE_p = ΔVq = E_T
So now we are looking to find the value of ΔVq. But what is q really? You might remember that current is defined as:
I = dq/dt
If we extract q from there we find that:
ΔE_T = ΔVq = VIt
We're almost done now... what's V then? Of course it's IR. So finally we get that:
ΔE_T = VIt = I^2Rt
Which is answer #2.