COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
2nd Edition
ISBN: 9781319414597
Author: Freedman
Publisher: MAC HIGHER
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Chapter 18, Problem 81QAP
To determine

(a)

The resistance of heater when it is applied 110V due to which 200g of water is heated from 20°C to 90°C

Expert Solution
Check Mark

Answer to Problem 81QAP

Resistance of heater is 30Ω.

Explanation of Solution

Given:

Potential difference across the heater = V=110V

Mass of water = m=200g=200g(1kg1000g)=0.2kg

Initial temperature of water = T1=20°C

Final temperature of water = T2=90°C

Specific heat of water = c=4186J/kg°C

Time up to heat is on = t=2.7min

Formula used:

Electrical energy consumed in heat is defined as,

  E=V2tR

  R is the resistance.

Heat absorbed by water due to temperature difference is defined as,

  Q=mc(T2T1)

Calculation:

It is given that 90% of electrical energy is consumed to heat the water, so,

  Q=90%ofEQ=0.9Emc(T2T1)=0.9V2tRR=0.9V2tmc(T2T1)

Now, substituting all these values,

  R=0.9× (110V)2×(162sec)0.2kg×4186 J/kgoC×(90°C20°C)=30.1Ω R=30Ω

Conclusion:

Thus, resistance of heater is 30Ω.

To determine

(b)

The difference in time interval when heater is connected with 12V of battery instead of 110V

Expert Solution
Check Mark

Answer to Problem 81QAP

The difference in time interval is 3h45min.

Explanation of Solution

Given:

Initial voltage across the heater = V1=110V

Initial time taken by heater to raise temperature of water with voltage 110V,

  t1=2.7min

Potential difference across the heater when it is connected by car's battery = V2=12V

Formula used:

Electrical energy consumed in heat is defined as,

  E=V2tR

Calculation:

Since, Electrical energy is defined as,

  E=V2tRV2=ERtWhen E and R are constant. then,V21t

Consider the time taken by car battery is t2, then,

  V1 2 V22=t2t1t2=V1 2 V22×t1t2= (110V)2 (12V)2×2.7mint2=226.9min227min

Time difference = t2t1=227min2.7min=224.3min

  t2t1=224.3min3h45min

Conclusion:

Thus, time difference is 3h45min.

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Chapter 18 Solutions

COLLEGE PHYSICS LL W/ 6 MONTH ACCESS

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