Glencoe Physics: Principles and Problems, Student Edition
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN: 9780078807213
Author: Paul W. Zitzewitz
Publisher: Glencoe/McGraw-Hill
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Question
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Chapter 22, Problem 99A

(a)

To determine

The amount of energy delivered to the heater in half an hour.

(a)

Expert Solution
Check Mark

Answer to Problem 99A

The energy drawn by the heater in half an hour is 0.9×106J .

Explanation of Solution

Given:

The electric heater is rated at 500W .

The power drawn by the heater is P=500W .

The time for which the heater operates is t=0.5h

Formula used:

The expression for the energy delivered to the heater is,

E=Pt

Here, P is the power used by the heater and t is the time of operation of the motor.

Calculation:

The power drawn by the heater is,

E=PtE=500W×0.5h×(3600s1h)E=0.9×106J

Conclusion:

Thus, the energy drawn by the heater in half an hour is 0.9×106J .

(b)

To determine

The change in the air temperature in half an hour.

(b)

Expert Solution
Check Mark

Answer to Problem 99A

The change in the temperature of the room in half an hour is 8.2°C .

Explanation of Solution

Given:

The mass of air in the room is m=50kg .

The specific heat of the air is C=1.10kJ/(kg°C) .

Consider the change in the temperature of the room is denoted by ΔT .

The percentage of thermal energy that warms up the room is 50% .

Formula used:

The expression for the change in the temperature (ΔT) of the room is,

H=mCΔTΔT=HmC

Here, m is the mass of the air in the room and C is the specific heat of the air.

Calculation:

Refer Part (a).

The energy drawn by the heater in half an hour is E=0.9×106J .

Consider the heat delivered by the heater to the room in half an hour is denoted by H .

The heat delivered by the heater to the room is 50% of heat drawn by the heater.

H=50%×EH=50100×0.9×106JH=4.5×105J×(1kJ103J)H=4.5×102kJ

The change in the temperature (ΔT) of the room in half an hour is,

ΔT=HmCΔT=4.5×102kJ(50kg)×1.10kJ/(kg°C)ΔT=4.5×105J(50kg)×1.10kJ/(kg°C)ΔT=8.18°CΔT8.2°C

Conclusion:

Thus, the change in the temperature of the room in half an hour is 8.2°C .

(c)

To determine

The cost of running the heater 6 hours per day for 30 days.

(c)

Expert Solution
Check Mark

Answer to Problem 99A

The cost of running the heater 6 hours per day for 30 days is $7 .

Explanation of Solution

Given:

The cost for 1kWh is $0.08 .

The heater runs 6h/day for 30 days.

Formula used:

Total cost will be the product of cost per kWh and total kWh consumed.

Calculation:

The total duration of operation (t) of the heater is,

t=(6hday)×30dayt=180h×(3600s1h)t=648,000s

The heater is rated at 500W . That is, the energy consumed by the heater per second is 500J

The energy consumed by the heater in time tis ,

EnergyConsumed=(500Js)×648,000sEnergyConsumed=324×106J

The cost for 1kWh is $0.08 .

The value of 1kWh is equivalent to 3.6×106J .

The cost for 3.6×106J is $0.08 .

The cost of running the heater 6 hours per day for 30 days is,

Cost=(324×106J3.6×106J)×$0.08Cost=$7

Conclusion:

Thus, the cost of running the heater 6 hours per day for 30 days is $7 .

Chapter 22 Solutions

Glencoe Physics: Principles and Problems, Student Edition

Ch. 22.1 - Prob. 11PPCh. 22.1 - Prob. 12PPCh. 22.1 - Prob. 13PPCh. 22.1 - Prob. 14PPCh. 22.1 - Prob. 15PPCh. 22.1 - Prob. 16PPCh. 22.1 - Prob. 17PPCh. 22.1 - Prob. 18PPCh. 22.1 - Prob. 19SSCCh. 22.1 - Prob. 20SSCCh. 22.1 - Prob. 21SSCCh. 22.1 - Prob. 22SSCCh. 22.1 - Prob. 23SSCCh. 22.1 - Prob. 24SSCCh. 22.1 - Prob. 25SSCCh. 22.2 - Prob. 26PPCh. 22.2 - Prob. 27PPCh. 22.2 - Prob. 28PPCh. 22.2 - Prob. 29PPCh. 22.2 - Prob. 30PPCh. 22.2 - Prob. 31PPCh. 22.2 - Prob. 32PPCh. 22.2 - Prob. 33PPCh. 22.2 - Prob. 34PPCh. 22.2 - Prob. 35SSCCh. 22.2 - Prob. 36SSCCh. 22.2 - Prob. 38SSCCh. 22.2 - Prob. 39SSCCh. 22.2 - Prob. 40SSCCh. 22.2 - Prob. 41SSCCh. 22 - Prob. 42ACh. 22 - Prob. 43ACh. 22 - Prob. 44ACh. 22 - Prob. 45ACh. 22 - Prob. 46ACh. 22 - Prob. 47ACh. 22 - Prob. 48ACh. 22 - Prob. 49ACh. 22 - Prob. 50ACh. 22 - Prob. 51ACh. 22 - Prob. 52ACh. 22 - Prob. 53ACh. 22 - Prob. 54ACh. 22 - Prob. 55ACh. 22 - Prob. 56ACh. 22 - Prob. 57ACh. 22 - Prob. 58ACh. 22 - Prob. 59ACh. 22 - Prob. 60ACh. 22 - Prob. 61ACh. 22 - Prob. 62ACh. 22 - Prob. 63ACh. 22 - Prob. 64ACh. 22 - Prob. 65ACh. 22 - Prob. 66ACh. 22 - Prob. 67ACh. 22 - Prob. 68ACh. 22 - Prob. 69ACh. 22 - Prob. 70ACh. 22 - Prob. 71ACh. 22 - Prob. 72ACh. 22 - Prob. 73ACh. 22 - Prob. 74ACh. 22 - Prob. 75ACh. 22 - Prob. 76ACh. 22 - Prob. 77ACh. 22 - Prob. 78ACh. 22 - Prob. 79ACh. 22 - Prob. 80ACh. 22 - Prob. 81ACh. 22 - Prob. 82ACh. 22 - Prob. 83ACh. 22 - Prob. 84ACh. 22 - Prob. 85ACh. 22 - Prob. 86ACh. 22 - Prob. 87ACh. 22 - Prob. 88ACh. 22 - Prob. 89ACh. 22 - Prob. 90ACh. 22 - Prob. 91ACh. 22 - Prob. 92ACh. 22 - Prob. 93ACh. 22 - Prob. 94ACh. 22 - Prob. 95ACh. 22 - Prob. 96ACh. 22 - Prob. 97ACh. 22 - Prob. 98ACh. 22 - Prob. 99ACh. 22 - Prob. 100ACh. 22 - Prob. 101ACh. 22 - Prob. 102ACh. 22 - Prob. 103ACh. 22 - Prob. 104ACh. 22 - Prob. 105ACh. 22 - Prob. 106ACh. 22 - Prob. 107ACh. 22 - Prob. 108ACh. 22 - Prob. 109ACh. 22 - Prob. 110ACh. 22 - Prob. 111ACh. 22 - Prob. 112ACh. 22 - Prob. 113ACh. 22 - Prob. 114ACh. 22 - Prob. 1STPCh. 22 - Prob. 2STPCh. 22 - Prob. 3STPCh. 22 - Prob. 4STPCh. 22 - Prob. 5STPCh. 22 - Prob. 6STPCh. 22 - Prob. 7STPCh. 22 - Prob. 8STPCh. 22 - Prob. 9STP
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