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In: Chemistry

Q1) The interior lighting of refrigerator is provided by incandescent lamps whose switches are actuated by...

Q1) The interior lighting of refrigerator is provided by incandescent lamps whose switches are actuated by the opening of the refrigerator door. Consider a refrigerator whose 50 W light bulb remains switched on continuously as a result of malfunction of the switch. If the refrigerator has a coefficient of performance of 1.25 and the cost of electricity is 9 pence per kWh, determine the increase in the energy consumption of the refrigerator and its cost per year (365 days) if the switch is not fixed. You may assume that the refrigerator is opened 30 times per day for an average of 20 seconds on each occasion.

Solutions

Expert Solution

(a) Calculating the total cost per year of the refrigerator without malfunction of the light switch :

Energy = Power x time (per year)

Power has unit as watt hence as given that the power used by the lamp is 50 W

Total time in hours per year while the refrigerator opens 30 times a day for an average of 20 seconds each occasion :

a day 30 times x av. 20 sec = [600 sec/ 60] min = 10 minutes per day

A year time utilised in hr = 10 min/day x 365 days = [3650 mins/ 60] hr = 60.833 hr/year

Energy (a) used per year = 50 x 60.633 = 3.04 kWh

Total cost (a) per year since 9 pence per KWh given = 9p x 3.04 kWh = 27.37p for units used

(b)

Calculating the total cost per year of the refrigerator with a malfunction of the light switch :

Energy = Power x time (per year)

Power has unit as watt hence as given that the power used by the lamp is 50 W

Total time in hours per year while the refrigerator opens 30 times a day for an average of 20 seconds each occasion :

a day = 1440 minutes per day

A year time utilised in hr = 1440 min/day x 365 days = [525600 mins/ 60] hr = 8760 hr/year

Energy (b) used per year = Power x time (per year) =50 W x 8760 hr  = 438000 W/1000 = 438 kWh

Total cost (b) per year since 9 pence per KWh given = 9p x 438 kWh = 39.42 GBP

Hence increase in energy consumption per year = [ energy (b) - energy (a)] = (438 - 3.04) kWh= 434.9 kWh

While increase in energy consumption per year = [Cost (b) - Cost (a)] = 39.14 GBP

queen_honey_blossom answered 1 year ago
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