Chapter U5.97, Problem 3E

(a)

Interpretation Introduction

Interpretation: The amount of calories of energy required to raise the temperature of 1 g of water by 5^oC needs to be determined.

Concept Introduction:

The amount of energy transferred for the given mass of substance can be calculated as follows:

  $q=mc\Delta T$

Here, m is mass, c is specific heat capacity and $\Delta T$ is change in temperature.

Answer to Problem 3E

5 cal.

Explanation of Solution

The specific heat capacity of water is $1.0{\text{ cal/g }}^{\text{o}}\text{C}$ .

The calories of energy required to raise the temperature of 1 g of water by 5 ^oC can be calculated as follows:

  $q=mc\Delta T$

Putting the values,

  $q=\left(1\text{ g}\right)\left(1.0{\text{ cal/g }}^{\text{o}}\text{C}\right)\left(5{}^{\text{o}}\text{C}\right)=5\text{ cal}$

Thus, the amount of energy required is 5 cal.

(b)

Interpretation Introduction

Interpretation: The amount of calories of energy required to raise the temperature of 2 g of water by 5^oC needs to be determined.

Concept Introduction:

The amount of energy transferred for the given mass of substance can be calculated as follows:

  $q=mc\Delta T$

Here, m is mass, c is specific heat capacity and $\Delta T$ is change in temperature.

Answer to Problem 3E

10 cal.

Explanation of Solution

The specific heat capacity of water is $1.0{\text{ cal/g }}^{\text{o}}\text{C}$ .

The calories of energy required to raise the temperature of 2 g of water by 5 ^oC can be calculated as follows:

  $q=mc\Delta T$

Putting the values,

  $q=\left(\text{2 g}\right)\left(1.0{\text{ cal/g }}^{\text{o}}\text{C}\right)\left(5{}^{\text{o}}\text{C}\right)=10\text{ cal}$

Thus, the amount of energy required is 10 cal.

(c)

Interpretation Introduction

Interpretation: The amount of calories of energy required to raise the temperature of 9 g of water by 35^oC needs to be determined.

Concept Introduction:

The amount of energy transferred for the given mass of substance can be calculated as follows:

  $q=mc\Delta T$

Here, m is mass, c is specific heat capacity and $\Delta T$ is change in temperature.

Answer to Problem 3E

315 cal.

Explanation of Solution

The specific heat capacity of water is $1.0{\text{ cal/g }}^{\text{o}}\text{C}$ .

The calories of energy required to raise the temperature of 9 g of water by 35 ^oC can be calculated as follows:

  $q=mc\Delta T$

Putting the values,

  $q=\left(\text{9 g}\right)\left(1.0{\text{ cal/g }}^{\text{o}}\text{C}\right)\left(35{}^{\text{o}}\text{C}\right)=315\text{ cal}$

Thus, the amount of energy required is 315 cal.