Answer the following questions:Show all your work. Include formulae and units! E

Question

Answer the following questions:Show all your work. Include formulae and units! EVERY TIME! Be sure to include meaningful,relavant diagram Don't try to squeeze everythingWrite down any formula used before plugging any numbers into it.

3. The specific heat of dry air is approximately 1000 J/kg?K. Suppose a room (under 1 atmosphere of pressure) measuring 10m X 10m X 3m is to be heated from an initial temperature of 170C to 270C. Assume that one mole of air has a mass of 28 grams.

a. How much energy must be supplied to the air to effect this change in temperature?Give your answer in Joules and kilowatt hours (kwh).

b. An electric heater must supply all the energy to heat the inside of your house.If an electric heater is 30% efficient, how much will it cost to heat up the room (one time!) if the cost of electricity is $0.12/kwh?

c. How much would it cost if a heat pump with a COP = 3.5 is used to heat the room instead of the electric heater?

Explanation / Answer

(a):

Q = mC(T2-T1)

m = molar mass * no. of moles

number of moles = PV/RT

m = molar mass* PV/RT

Q = molar mass* (PV/RT)*C*(T2 - T1) note : all temp must be in kelvin

Q = 1084 Jules = 301.1*10^(-6) kwh

(b):

efficiency = 30%

Heat suplied by heater *30 / 100 = 301.1*10^(-6)

heat supplied by heater = 1.0037 * 10^(-3) kwh

cost = rate * heat supplied by heater

cost = 0.12 * 1.0037 * 10^(-3)

cost = 0.1204 * 10^(-3) $

(c):

Heat required in case of heat pump * 3/5 = 301.1*10^(-6)

Heat required in case of heat pump = 501.833*10^(-6) kwh

cost = 0.12*501.833*10^(-6) = 0.06022 *10^(-3) $

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