Chapter 10, Problem 68A

(a)

Interpretation Introduction

Interpretation: The amount of heat absorbed by the water needs to be determined.

Concept introduction: Due to change in temperature, the flow of energy is termed as heat. It depends on the pathway. Heat is expressed in energy units usually calories and joules.

Answer to Problem 68A

The amount of heat that is absorbed by the water is 1460.25 J.

Explanation of Solution

Given mass of water is 100 g

Initial temperature is $\text{21}\text{.31}°\text{C}$

Final temperature is $\text{24}\text{.80}°\text{C}$

Thus, the change in temperature is as follows:

  $\begin{array}{c}\Delta \text{T=24}\text{.80}°\text{C}-21.31°\text{C}\\ \text{=3}\text{.49}°\text{C}\end{array}$

Specific heat of water is $\text{4}\text{.184}\text{J}/\text{g°C}$

The expression for heat is as follows:

  $\text{Q=m×s×ΔT}$

Here, Q is heat capacity, s is specific heat capacity, m is mass of the sample, and $\text{ΔT}$ is change in temperature.

Put the values in above equation is as follows:

  $\begin{array}{c}\text{Q=100}\cancel{\text{g}}\text{×4}\text{.184}\frac{\text{J}}{\cancel{\text{g}}\cancel{\text{°C}}}\text{×3}\text{.49}\cancel{°\text{C}}\\ =1460.25\text{J}\end{array}$

Thus, the amount of heat that is absorbed by the water is 1460.25 J.

(b)

Interpretation Introduction

Interpretation: The heat absorbed by water needs to be compared with the heat lost by the metal.

Concept introduction: Due to change in temperature, the flow of energy is termed as heat. It depends on the pathway. Heat is expressed in energy units usually calories and joules.

Answer to Problem 68A

Heat given by metal = Heat absorbed by water

Explanation of Solution

Heat always moves from hotter to cooler object. Heat absorbed by water is equal to heat given by the metal.

(c)

Interpretation Introduction

Interpretation: Initial temperature of hot metal and final temperature of metal is to be calculated.

Concept introduction: Due to change in temperature, the flow of energy is termed as heat. It depends on the pathway. Heat is expressed in energy units usually calories and joules.

Answer to Problem 68A

Initial temperature of ‘hot’ metal is $\text{100}°\text{C}$ and final temperature of metal is $24.8°\text{C}$ .

Explanation of Solution

Metal is taken from boiling water. Thus initial temperature of ‘hot’ metal is $\text{100}°\text{C}$ . Given final temperature of water is $24.8°\text{C}$ .Final temperature of metal and water is equal. Thus, final temperature of metal is $24.8°\text{C}$ .

(d)

Interpretation Introduction

Interpretation: The specific heat capacity of the metal is to be calculated.

Concept introduction: Due to change in temperature, the flow of energy is termed as heat. It depends on the pathway. Heat is expressed in energy units usually calories and joules.

Answer to Problem 68A

Specific heat of the metal is $0.388\frac{\text{J}}{\text{g}°\text{C}}$ .

Explanation of Solution

Given mass of the metal (m) =50g.

Heat lost by metal (Q) =1460.2J

Change in temperature of metal is as follows:

  $\begin{array}{c}\left(\Delta \text{T}\right)=100°\text{C}-24.8°\text{C}\\ =75.2°\text{C}\end{array}$

The expression for heat is as follows:

  $\text{Q=m×s×ΔT}$

Here Q is heat capacity, s is specific heat capacity, m is mass of the sample, and $\text{ΔT}$ is change in temperature

Put the values in above equation as follows:

  $\begin{array}{c}\text{1460}\text{.2J=50g×s×75}\text{.2}°\text{C}\\ \text{s}=0.388\frac{\text{J}}{\text{g}\times °\text{C}}\end{array}$

Thus, specific heat of the metal is $0.388\frac{\text{J}}{\text{g}°\text{C}}$ .

(e)

Interpretation Introduction

Interpretation: From given specific heat capacity the metal is to be determined. 

Concept introduction: Due to change in temperature, the flow of energy is termed as heat. It depends on the pathway. Heat is expressed in energy units usually calories and joules.

Answer to Problem 68A

The metal is zinc.

Explanation of Solution

Given specific heat capacity of tin, zinc and aluminum are $\text{0}\text{.227}\text{J}/\text{g°C}\text{,}\text{0}\text{.388}\text{J}/\text{g°C}\text{and0}\text{.891}\text{J}/\text{g°C}$ .

Specific heat capacity depends on nature of the substance. Specific heat capacity of given metal is same as zinc. Thus, the metal is zinc.