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 48.4 V to nichrome wire of total resistance 8.14 . (a) Find the current carried by the wire and the power rating of the heater. 1=15.9 P = 288 (b) Using this heater, how long would it take to heat 2.60 x 10 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 R. (c) How many kilowatt-hours of electricity are used during the time calculated in part (b) and at what cost, at $0.14 per kilowatt-hour? U= kWh cost

Explanation / Answer

According to the concept of the thermal electricity

Heat Q=nCv(T2-T1)

Given that

Resistance R=8.14 ohm

Potential difference V=48.4 v

Now we find the heat

Heat Q=2.6*10^3*5/2*8.3*(25-10)=539.5*10^3 J

Now we find the time taken

V^2/R=Q/t

48.4^2/8.14=539.5*10^3/t

Time t=539.5*10^3*8.14/48.4^2=1874.7 sec

Now we find electric energy

Energy =V^2*t/R=48.4^2*1874.7/8.14=539508.3 J

=539508.3*2.778*10^-7 (1J=2.778*10^-7 KWh)

=0.15 Kilo watt hour

Cost =0.15*0.14=0.021

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