   Chapter 20, Problem 30PS

Chapter
Section
Textbook Problem

Microwave ovens are highly efficient, compared to other cooking appliances. A 1100-watt microwave oven, running at full power for 90 seconds, will raise the temperature of 1 cup of water (225 mL) from 20 °C to 67 °C. As a rough measure of the efficiency of the microwave oven, compare its energy consumption with the energy required to raise the water temperature.

Interpretation Introduction

Interpretation: The efficiency of the microwave oven by comparing energy consumption with energy required to raise the water temperature should be determined from the given data.

Concept introduction:

Microwave oven: Conversion of electric energy into microwave energy is the basis of microwave oven. It consumes lesser energy than gas stove, but cost will be higher for microwave oven usage.

%efficiency=energyabsorbedbywaterenergyreleasedbythehotplate

Energyabsorbedbywaterinjoules=massofthewater(g)×ΔT°C×4.18Jg°CEnergyreleasedbyhotplateinjoules=Totalhotplatewattage(watts)×time(s)×[1J/swatt]

Explanation

Given:

Totalhotplatewattage=1100watttime=90sΔT=67°C20°C=47°CVolumeofwater=225ml=225g

The energy absorbed by the water is,

Energyabsorbedbywaterinjoules=massofthewater(g)×ΔT°C×4.18Jg°C=225g×47°C×4.18Jg°C=44

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