Chapter 14, Problem 17P

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?

To determine

Part(a)To determine:

Heat capacity in terms of specific heat

Answer to Problem 17P

Solution:

Heat capacity in terms of specific heat is $Cp=mcp$

Explanation of Solution

Formula Used:

The formula used is the relation between temperature and specific heat from thermodynamics

$Q=mcp(Tf-Ti)$

Where,

$Q$ is the heat transferred

$cp$ is the specific heat

$m$ is the mass

$Tf$ is the final temperature

$Ti$ is the initial temperature

Calculation:

The specific heat capacity formula is: $Q=mcp(Tf-Ti)$

where $cp$ is the specific heat.

The heat capacity formula is: $Q=Cp(Tf-Ti)$

where $Cp$ is the specific heat.

Dividing the equations above we get

$\frac{Q}{Q}=\frac{mcp(Tf-Ti)}{Cp(Tf-Ti)}$

$1=\frac{mcp}{Cp}$

$Cp=mcp$

Thus, the heat capacity is related to the specific heat by $Cp=mcp$

To determine

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:

$cp$ for water is 4186 J/kgk

$m$ is mass of water which is 1 kg

Formula Used:

The relation between heat capacity and specific heat by $Cp=mcp$

$Cp$ is the heat capacity

$cp$ is the specific heat

$m$ is the mass

Calculation:

The heat capacity is related to the specific heat by $Cp=mcp$

Substituting the following:

$cp$ for water is 4186 J/kgk

$m$ is mass of water which is 1 kg

$Cp=1(4186)$

$Cp=4186$ J/k

To determine

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:

$cp$ for water is 4186 J/kgk

$m$ is mass of water which is 45 kg

Formula Used:

The relation between heat capacity and specific heat by $Cp=mcp$

$Cp$ is the heat capacity

$cp$ is the specific heat

$m$ is the mass

Calculation:

The heat capacity is related to the specific heat by $Cp=mcp$

Substituting the following:

$cp$ for water is 4186 J/kgk

$m$ is mass of water which is 45 kg

$Cp=45(4186)$

$Cp=\text{188370}$ J/k