Concept explainers
The heat capacity, C, ofan object is defined as the amount of heat needed to raise its temperature by 1 C°. Thus, to raise the temperature by ΔT requires heat Q given by
Q = C ΔT.
a. Write the heat capacity C in terms of the specific heat, c, of the material,
b.What is the heat capacity of 1.0 kg of water?
c.Of 45 kg of water?
Part(a)To determine:
Heat capacity in terms of specific heat
Answer to Problem 17P
Solution:
Heat capacity in terms of specific heat is
Explanation of Solution
Formula Used:
The formula used is the relation between temperature and specific heat from thermodynamics
Where,
is the heat transferred
is the specific heat
is the mass
is the final temperature
is the initial temperature
Calculation:
The specific heat capacity formula is:
where is the specific heat.
The heat capacity formula is:
where is the specific heat.
Dividing the equations above we get
Thus, the heat capacity is related to the specific heat by
Part(b)To determine:
Heat capacity of 1 kg of water
Answer to Problem 17P
Solution:
Heat capacity of 1 kg of water is 4186 J/k
Explanation of Solution
Given:
for water is 4186 J/kgk
is mass of water which is 1 kg
Formula Used:
The relation between heat capacity and specific heat by
is the heat capacity
is the specific heat
is the mass
Calculation:
The heat capacity is related to the specific heat by
Substituting the following:
for water is 4186 J/kgk
is mass of water which is 1 kg
J/k
Part(c)To determine:
Heat capacity of 45 kg of water
Answer to Problem 17P
Solution:
Heat capacity of 45 kg of water is 188370 J/k
Explanation of Solution
Given:
for water is 4186 J/kgk
is mass of water which is 45 kg
Formula Used:
The relation between heat capacity and specific heat by
is the heat capacity
is the specific heat
is the mass
Calculation:
The heat capacity is related to the specific heat by
Substituting the following:
for water is 4186 J/kgk
is mass of water which is 45 kg
J/k
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Physics: Principles with Applications
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