Question

1. A 120 V potential difference is applied to a space heater whose resistance is 19.8 Ω when hot. At what rate is electrical energy being transferred to thermal energy?

2. How much thermal energy is produced in 4.2 hours?

3. If electricity costs 10.0 cents per kW·h, how much does it cost to operate the device for 4.2 hours?

Answer 1

Given

V = 120 V

R = 19.8 ohm

1.

the rate at which the electrical energy being transferred to thermal energy is P = v^2/R

here the energy rate is power , which is power dissipation at the resistor in the form of heat  

P = 120^2/19.8 W

P = 727.273 W

2.

thermal energy produced in 4.2 hours = 4.2*60*60 s = 15120 s

E = P*t

E = 727.273*15120 J

E = 10996367.76 J

the thermal energy produced in 4.2 hrs is 10996367.76 J

3. 3.0545466 kWh

we know that 1 kWh = 3.6*10^6 J

so 10996367.76 J = 3.0545466 kWh

the cost is 120*3.0545466 kWh = 366.545592 cents = $ 3.66545592