Chapter 5, Problem 1DE

One of the important ideas of thermodynamics is that energy can be transferred in the form of heat or work. Imagine that you lived 180 years ago when the relationships between heat and work were not well understood. You have formulated a hypothesis that work can be converted to heat with the same amount of work always generating the same amount of heat. To test this idea, you have designed an experiment using a device in which a falling weight is connected through pulleys to a shaft with an attached paddle wheel that is immersed in water. This is actually a classic experiment performed by James Joule in the 1840s. You can see various images of Joule's apparatus by searching the Internet for "Joule experiment images."

1. Using this device, what measurements would you need to make to test your hypothesis?
2. What equations would you use in analyzing your experiment?
3. Do you think you could obtain a reasonable result from a single experiment? Why or why not?
4. In what way could the precision of your instruments affect the conclusions that you make?
5. List ways that you could modify the equipment to improve the data you obtain if you were performing this experiment today instead of 180 years ago.
6. Give an example of how you could demonstrate the relationship between heat and a form of energy other than mechanical work.

Interpretation Introduction

Interpretation: The balanced equations for the given reaction statements are to be identified.

Concept introduction: The relation of the work and the heat produced is calculated by the Joule experiment. The mechanical equivalent of heat is the ratio of the heat produced from the mechanical work.

(a)

To determine: The measurements required to test the hypothesis using device of Joule’s experiment.

Answer to Problem 1DE

Solution: The measurements required to test the hypothesis using device of Joule’s experiment is stated below.

Explanation of Solution

The setup required for the experiment is,

Figure 1

The relation between the work done and the heat produced is calculated in the following manner.

Using the above setup, the mechanical work is obtained by using potential energy lost by the falling mass.

Therefore, work done is equal to the potential energy of the falling mass.

Thus, the work done is calculated by the formula,

$\text{Mechanical}\text{Work}=\text{Total}\text{mass}\text{of}\text{objects}\times \text{accelaration}\text{due}\text{to}\text{gravity}\times \text{height}\text{of}\text{mass}$

The heat that is generated in the mass of water in the calorimeter chamber is calculated by the formula,

$\text{Heat}=\left(\text{Mass}\text{of}\text{water xWater}\text{equivalent}\text{of}\text{calorimeter}\right)\left(\text{Change}\text{in}\text{temperature}\right)$

where, water equivalent of calorimeter is the amount of water that absorbs the same amount of heat as the calorimeter to raise the temperature by one degree.

For the comparison of the work done with heat, the measurements that we need is,

• Mass of the falling object.
• Mass of water in the calorimeter.
• Height of the falling mass.
• Change in temperature.
• Water equivalent of calorimeter.

Conclusion

For the comparison of the work done with heat, the measurements that we need is,

• Mass of the falling object.
• Mass of water in the calorimeter.
• Height of the falling mass.
• Change in temperature.
• Water equivalent of calorimeter.

Interpretation Introduction

To determine: The equations used to analyze the experiment.

Answer to Problem 1DE

Solution: The equations used to analyze the experiment are stated below.

Explanation of Solution

The relation between the work done and the heat produced is to be determined.

Using the above setup, the mechanical work is obtained by using potential energy lost by the falling mass.

Therefore, work done is equal to the potential energy of the falling mass.

Thus, the work done is calculated by the formula,

$\text{Mechanical}\text{Work}=\text{Total}\text{mass}\text{of}\text{objects}\times \text{accelaration}\text{due}\text{to}\text{gravity}\times \text{height}\text{of}\text{mass}$

The heat that is generated in the mass of water in the calorimeter chamber is calculated by the formula,

$\text{Heat}=\left(\text{Mass}\text{of}\text{water}+\text{Water}\text{equivalent}\text{of}\text{calorimeter}\right)\left(\text{Change}\text{in}\text{temperature}\right)$

The ratio of the work done in generating heat is calculated by the formula,

$\frac{\text{Mechanical}\text{Work}}{\text{Heat}}=\text{Constant}$

Here, the constant is called as mechanical equivalent of heat.

Conclusion

The equations used to analyze the experiment are of mechanical work, heat and their ratio.

Interpretation Introduction

To determine: If the reasonable result is obtained from a single experiment.

Answer to Problem 1DE

Solution: No.

Explanation of Solution

The given experiment determines the relation of amount of work that is converted into heat energy.

This should be applicable for all sets of systems of thermodynamics.

Therefore, the same relation should be obtained in different setups of experiments.

Hence, the reasonable results are not obtained by single experiment.

Conclusion

The reasonable results are not obtained by single experiment.

Interpretation Introduction

To determine: The effect of precision of the instruments on the conclusion.

Answer to Problem 1DE

Solution: The precision in the measurement of the heat produced from work should be accurate for the perfect conclusion.

Explanation of Solution

The given experiment determines the relation of amount of work that is converted into heat energy.

The error that may occur is the loss of heat from the system. Therefore, the system should be properly isolated to measure appropriate heat.

Therefore, the precision in the measurement of the heat produced from work should be accurate for the perfect conclusion.

Conclusion

The precision in the measurement of the heat produced from work should be accurate for the perfect conclusion.

Interpretation Introduction

To determine: The modifications in the experiment that are done considering available modern amenities.

Answer to Problem 1DE

Solution: The modifications in the experiment that are done considering available modern amenities are using automated mechanical paddle stirrer and digital calorimeter.

Explanation of Solution

The mechanical work in the ancient experiment is performed by the falling masses.

Nowadays, automated mechanical paddle stirrer is available, that can be used to create mechanical work.

Also, the digital calorimeter is available that detects the change in temperature appropriately and provides an isolated system.

Conclusion

The modifications in the experiment that are done considering available modern amenities are using automated mechanical paddle stirrer and digital calorimeter.

Interpretation Introduction

To determine: The example that demonstrates the relationship between heat and a form of energy other than mechanical work.

Answer to Problem 1DE

Solution: The relationship between heat and a form of energy other than mechanical work is,

  $\text{Heat}=\text{Mechanical}\text{Work}\times \text{Mechanical}\text{equivalent}\text{of}\text{heat}$

Explanation of Solution

In the above experiment, the water is stirred using a paddle with a known falling mass. The water is placed isolated in a calorimeter and a thermometer measures the temperature change in it.

The rotation in the water is obstructed by the vanes in the container. This causes the rise in temperature of water that is measured using thermometer.

The rise in temperature with the mechanical work is measured.

The relation between the work done and the heat produced is calculated in the following manner.

Using the above setup, the mechanical work is obtained by using potential energy lost by the falling mass.

Therefore, work done is equal to the potential energy of the falling mass.

Thus, the work done is calculated by the formula,

$\text{Mechanical}\text{Work}=\text{Total}\text{mass}\text{of}\text{objects}\times \text{accelaration}\text{due}\text{to}\text{gravity}\times \text{height}\text{of}\text{mass}$

The heat that is generated in the mass of water in the calorimeter chamber is calculated by the formula,

$\text{Heat}=\left(\text{Mass}\text{of}\text{water}+\text{Water}\text{equivalent}\text{of}\text{calorimeter}\right)\left(\text{Change}\text{in}\text{temperature}\right)$

Where, Water equivalent of calorimeter is the amount of water that absorbs the same amount of heat as the calorimeter to raise the temperature by one degree.

The ratio of the work done in generating heat is calculated by the formula,

$\frac{\text{Mechanical}\text{Work}}{\text{Heat}}=\text{Constant}$

Here, the constant is called as mechanical equivalent of heat.

Therefore, mechanical equivalent of heat is the form of energy.

The above equation is modified as,

$\text{Heat}=\text{Mechanical}\text{Work}\times \text{Mechanical}\text{equivalent}\text{of}\text{heat}$

Conclusion

The relationship between heat and a form of energy other than mechanical work is,

  $\text{Heat}=\text{Mechanical}\text{Work}\times \text{Mechanical}\text{equivalent}\text{of}\text{heat}$