Chapter 6, Problem 6.76E

Using the specific heat data of Table 6.8, calculate the amount of heat (in calories) needed to increase the temperature of the following:

a. $50.\text{g}$ of aluminum from $25°\text{C}$ to $55°\text{C}$

b. $2.50\times {10}^3\text{g}$ of ethylene glycol from $80.°\text{C}$ to $85°\text{C}$

c. $500.\text{g}$ of steam from $110.°\text{C}$ to $120.°\text{C}$

Interpretation Introduction

(a)

Interpretation:

The amount of heat (in calories) required to increase the temperature of $50\text{g}$ aluminum from $25°\text{C}$ to $55°\text{C}$ is to be calculated.

Concept introduction:

When temperature is changed or the state of matter is changed the energy is either absorbed or released. The energy required to change temperature of matter is known as specific heat of matter. The energy required to change a state of matter is known as heat of fusion or vaporization.

Answer to Problem 6.76E

The amount of heat (in calories) required to increase the temperature of $50\text{g}$ aluminum from $25°\text{C}$ to $55°\text{C}$ is $360\text{cal}$.

Explanation of Solution

The formula to calculate amount of heat (in calories) required to increase the temperature is given below as,

$\text{Heat}=\left(\text{sample}\text{mass}\right)\left(\text{specific}\text{heat}\right)\left(\text{temperature}\text{change}\right)$

Substitute the values in the above equation as follows.

$\begin{array}{rll}\text{Heat}& =& \left(\text{sample}\text{mass}\right)\left(\text{specific}\text{heat}\right)\left(\text{temperature}\text{change}\right)\\ & =& \left(50\text{g}\right)\left(\frac{\text{0}\text{.24}\text{cal}}{\text{g°C}}\right)\left(55°\text{C}-25°\text{C}\right)\\ & =& \left(50\text{g}\right)\left(\frac{\text{0}\text{.24}\text{cal}}{\text{g°C}}\right)\left(30°\text{C}\right)\\ & =& 360\text{cal}\end{array}$

Conclusion

The amount of heat (in calories) required to increase the temperature of $50\text{g}$ aluminum from $25°\text{C}$ to $55°\text{C}$ is $360\text{cal}$.

Interpretation Introduction

(b)

Interpretation:

The amount of heat (in calories) required to increase the temperature of $2.50\times {10}^3\text{g}$ ethylene glycol from $80°\text{C}$ to $85°\text{C}$ is to be calculated.

Concept introduction:

When temperature is changed or the state of matter is changed the energy is either absorbed or released. The energy required to change temperature of matter is known as specific heat of matter. The energy required to change a state of matter is known as heat of fusion or vaporization.

Answer to Problem 6.76E

The amount of heat (in calories) required to increase the temperature of $2.50\times {10}^3\text{g}$ ethylene glycol from $80°\text{C}$ to $85°\text{C}$ is $7.125\times {10}^3\text{cal}$.

Explanation of Solution

The formula to calculate amount of heat (in calories) required to increase the temperature is given below as,

$\text{Heat}=\left(\text{sample}\text{mass}\right)\left(\text{specific}\text{heat}\right)\left(\text{temperature}\text{change}\right)$

Substitute the values in the above equation as follows.

$\begin{array}{rll}\text{Heat}& =& \left(\text{sample}\text{mass}\right)\left(\text{specific}\text{heat}\right)\left(\text{temperature}\text{change}\right)\\ & =& \left(2.50\times {10}^3\text{g}\right)\left(\frac{\text{0}\text{.57}\text{cal}}{\text{g°C}}\right)\left(85°\text{C}-80°\text{C}\right)\\ & =& \left(2.50\times {10}^3\text{g}\right)\left(\frac{\text{0}\text{.57}\text{cal}}{\text{g°C}}\right)\left(5°\text{C}\right)\\ & =& 7.125\times {10}^3\text{cal}\end{array}$

Conclusion

The amount of heat (in calories) required to increase the temperature of $2.50\times {10}^3\text{g}$ ethylene glycol from $80°\text{C}$ to $85°\text{C}$ is $7.125\times {10}^3\text{cal}$.

Interpretation Introduction

(c)

Interpretation:

The amount of heat (in calories) required to increase the temperature of $500\text{g}$ steam from $110°\text{C}$ to $120°\text{C}$ is to be calculated.

Concept introduction:

When temperature is changed or the state of matter is changed the energy is either absorbed or released. The energy required to change temperature of matter is known as specific heat of matter. The energy required to change a state of matter is known as heat of fusion or vaporization.

Answer to Problem 6.76E

The amount of heat (in calories) required to increase the temperature of $500\text{g}$ steam from $110°\text{C}$ to $120°\text{C}$ is $2400\text{cal}$.

Explanation of Solution

The formula to calculate amount of heat (in calories) required to increase the temperature is given below as,

$\text{Heat}=\left(\text{sample}\text{mass}\right)\left(\text{specific}\text{heat}\right)\left(\text{temperature}\text{change}\right)$

Substitute the values in the above equation as follows.

$\begin{array}{rll}\text{Heat}& =& \left(\text{sample}\text{mass}\right)\left(\text{specific}\text{heat}\right)\left(\text{temperature}\text{change}\right)\\ & =& \left(500\text{g}\right)\left(\frac{\text{0}\text{.48}\text{cal}}{\text{g°C}}\right)\left(120°\text{C}-110°\text{C}\right)\\ & =& \left(500\text{g}\right)\left(\frac{\text{0}\text{.48}\text{cal}}{\text{g°C}}\right)\left(10°\text{C}\right)\\ & =& 2400\text{cal}\end{array}$

Conclusion

The amount of heat (in calories) required to increase the temperature of $500\text{g}$ steam from $110°\text{C}$ to $120°\text{C}$ is $2400\text{cal}$.