Making your own immersion heater. Tired of having his morning cup of coffee go cold, an...

Making your own immersion heater. Tired of having his morning cup of coffee go cold, an enterprising young physics major decides to build an immersion heater (see Problem 112) out of batteries and a 1.0-m length of 32-gauge (0.20-mm diameter) copper wire. By coiling up the copper wire so that it can fi t in a coffee cup and connecting the coil to several 9-V batteries connected in series, the coil of wire will heat up and in turn heat the coffee in the cup. Estimate the number of batteries this student will need to heat up a cup of coffee from room temperature to a reasonable drinking temperature (90°C) in a reasonable amount of time.

(reference problem 112)

Heating a cup of tea. Figure P19.112A shows an immersion heater. It is just a small coil with a resistance R that is used to heat a beverage such as a cup of tea. The heater is connected to a source of emf causing heat to be dissipated in the resistor that heats the tea (Fig. P19.112B). If a cup of tea is initially at room temperature and the immersion heater is able to heat the tea to boiling in 180 s, estimate R. Assume the heater is connected to an emf with V = 110 V.