Question

An immersion heater used to boil water for a single cup of tea plugs into a 120 V outlet and is rated at 450 W . Suppose your super-size, super-insulated tea mug contains 400 g of water at a temperature of 23 ∘C. You can ignore the energy needed to raise the temperature of the mug and the heater itself.

What is the resistance of the heater?

How long will this heater take to bring the water to a boil?

Answer 1

The resistance of the immersion heater is 32 ohms. To bring 400 g of water from 23 °C to a boiling point, it will take approximately 4.78 minutes using the 450 W rated heater.

Step-by-step explanation:

The student has an immersion heater rated at 450 W that plugs into a 120 V outlet and 400 g of water at 23 °C to bring to a boil. First, we need to calculate the resistance of the heater. Using the formula Power (P) = Voltage (V)² / Resistance (R), we can rearrange to find resistance: R = V² / P. Thus, R = (120 V)² / 450 W, which equals 32 ohms. To find how long it will take to bring the water to a boil, we should calculate the amount of heat required and then use the power rating of the heater. The heat needed is given by Q = mcΔT, where m is the mass of the water, c is the specific heat capacity of water (4.184 J/g°C), and ΔT is the change in temperature. For 400 g of water raised from 23 °C to 100 °C (ΔT = 77 °C), Q = 400 g * 4.184 J/g°C * 77 °C = 128982.4 J. The power rating determines how fast this heat can be delivered, so the time t required is Q / P. So, t = 128982.4 J / 450 W = 286.63 seconds, or approximately 4.78 minutes.

Answer 2

Step-by-step explanation:

Given

Voltage
`V=120 V`

Power
`P=450 W`

mass of water
`m=400 gm`

initial temperature of water
`T_i=23^(\circ)C`

Resistance R is given by

`P=(V^2)/(R)`

`R=(V^2)/(P)`

`R=(120^2)/(450)`

`R=32 \ Omega`

Heat required to raise water temperature to
`100^(\circ)C`

`Q=mc\Delta T`

where
`c=4.184 kJ/kg-K` specific heat of water

`Q=0.4* 4.184* (100-23)=128.86 kJ`

time required is

`t=(Q)/(P)=(128.86* 1000)/(450)`

`t=286.37 s\approx 4.77 min`