Use the worked example above to help you solve this problem. An electrical heate

Question

Use the worked example above to help you solve this problem. An electrical heater is operated by applying a potential difference of 51.5 V to nichrome wire of total resistance 8.28 .

(a) Find the current carried by the wire and the power rating of the heater. I = A P = W

(b) Using this heater, how long would it take to heat 2.70 103 moles of diatomic gas (e.g., a mixture of oxygen and nitrogen, or air) from a chilly 10°C to 25°C? Take the molar specific heat at constant volume of air to be 5 2 R. s

(c) How many kilowatt-hours of electricity are used during the time calculated in part (b) and at what cost, at $0.13 per kilowatt-hour? U = kWh cost $

Explanation / Answer

a)

Current carried by wire

I=V/R =51.5/8.28 =6.22 A

Power rating of the heater

P=I2R=6.222*8.28 =320.32 Watts

b)

Amount of heat transferred

Q=nCv(T2-T1)=(2.7*103)*(5/2)*8.314*(25-10)=8.4*105 Joules

Time taken by the heater to heat

t=Q/P =8.4*105/320.32

t=2.628*103 s

c)

Energy in KWH

Q=8.4*105/1000*(3600) =0.2338 KWH

Cost =0.13*0.2338 =$0.0304

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