Explanation Given info: The mass of the water is 1.000 g , value of c 0 is 4207.9 J / kg ⋅ K , value of a is − 1.292 J / kg ⋅ K 2 and the value of b is 00133 J / kg ⋅ K 3 Write the expression for the heat required to raise the temperature of the water to to T 2 . Q = ∫ T 1 T 2 m c ( T ) d T Here, d Q is the amount of heat energy to raise d T temperature m is the mass of the water c ( T ) is the specific heat in terms of temperature d T is the temperature difference T 1 and T 2 are the initial and final temperature respectively Substitute c 0 + a T + b T 2 for c ( T ) in above equation to modify the equation. Q = ∫ T 1 T 2 m ( c 0 + a T + b T 2 ) d T Integrate the above equation with respect T from 0 ° C to 100 ° C to get heat required to raise the temperature from 0 ° C to 100 ° C . Therefore substitute 0 ° C for T 1 , 100 ° C for T 2 and 1.000 g for m to get Q . Q = ∫ 0 100 m ( c 0 + a T + b T 2 ) d T Q = 1.000 kg [ 100 c 0 + a ( 100 ) 2 2 + b ( 100 ) 3 3 ] Substitute 4207.9 J / kg ⋅ K for c 0 , − 1.292 J / kg ⋅ K 2 for a and 0.0133 J / kg ⋅ K 3 for b in above equation to get Q . Q = 1.000 kg [ 100 ( 4207.9 J / kg ⋅ K ) + ( − 1.292 J / kg ⋅ K 2 ) ( 100 ) 2 2 + ( 0

Essential University Physics (3rd Edition)

3rd Edition

ISBN: 9780134202709

Author: Richard Wolfson

Publisher: PEARSON

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Question

Chapter 16, Problem 73P

To determine

The percentage difference between the heat energy required to raise the temperature of 1.000 kg of water from 0° C 100 ° C by using c(T)=c0+aT+bT2 and by using 4184 J/kg⋅K .

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Chapter 16, Problem 72P

Chapter 16, Problem 74P

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Chapter 16 Solutions

Essential University Physics (3rd Edition)

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The percentage difference between the heat energy required to raise the temperature of 1.000 kg of water from 0 ° C 100 ° C by using c ( T ) = c 0 + a T + b T 2 and by using 4184 J / kg ⋅ K .

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The percentage difference between the heat energy required to raise the temperature of 1.000 kg of water from 0° C 100 ° C by using c(T)=c0+aT+bT2 and by using 4184 J/kg⋅K .

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Chapter 16 Solutions