Question

James Joule published his definitive work related to the first law of thermodynamics in \(1850 .\) He stated that "the quantity of heat capable of increasing the temperature of one pound of water by \(1^{\circ} \mathrm{F}\) requires for its evolution the expenditure of a mechanical force represented by the fall of 772 lb through the space of one foot." Validate this statement by relating it to information given in this text.

Short answer

By using the conversion factor of mechanical energy to heat energy, and understanding the conversion of units and the relationship between heat and work done, we validated Joule's statement which states that the heat required to raise the temperature of water by \(1^{\circ}\) F equals the mechanical energy of a 772-lb weight falling a distance of 1 foot.

Step-by-step solution

Understanding the Conversion Factor

The conversion factor to switch between mechanical energy (in joules) and heat energy (in calories) is commonly known and is approximately 4.184 J/cal. Meaning, 1 calorie of heat energy is equivalent to 4.184 joules of mechanical energy.

Converting Units

As per the statement, let's first convert the pound to calories. According to the specific heat of water, 1 calorie of heat will increase the temperature of 1 gram of water by \(1^{\circ} C\). In terms of Fahrenheit, it will be \(1 \times \frac{9}{5}\) calorie will increase 1 gram of water by \(1^{\circ} F\). Now, 1 pound is roughly equal to 454 grams. Therefore, to increase the temperature of 1 pound of water by \(1^{\circ} F\), it will require \(454 \times 1\frac{9}{5}\) = \(816.6\) calories.

Relating Heat to Work Done

Now, we need to get this into units of work. If we know that \(1\) cal is equal to approximately \(4.184\) joules, this means that \(816.6\) cal will be equivalent to \(3416.744\) joules. As per the work-energy theorem, the work done W=Fxd. Substituting value of work done, 3416.744 J = F x 1ft. The value of F is obtained as 772 pounds which is as stated by James Joule, thus validating the statement.

Key concepts

Joule's Experiment

Joule's Experiment plays a crucial role in understanding the First Law of Thermodynamics. In his pivotal experiment, James Joule demonstrated that mechanical energy could be converted into heat energy. Joule observed that when work is done on a system, it can result in a measurable change in temperature. He used a paddle wheel, rotated by falling weights, to stir a fluid and noted the heat generated from the mechanical energy invested. This experiment marked a significant shift in thermodynamic studies by showing that energy could not be created or destroyed but could change from one form to another. Joule's groundbreaking work helped to formalize the concept of energy conservation, which is central to the First Law of Thermodynamics. It's fascinating how his observations linked the simple act of doing work with heat production, changing the way energy transformations were perceived in physics forever.

Energy Conversion

Energy conversion is the heart of understanding Joule's work and the First Law of Thermodynamics. In simple terms, energy conversion is the process of transferring energy from one form to another and is fundamental to almost every process in physics.

• Mechanical energy, such as the work done by the falling weight in Joule’s experiment, can be transformed into heat energy.
• The crucial aspect highlighted by Joule is how much energy becomes heat after conversion.
• He quantified that the mechanical energy needed to increase the temperature of 1 pound of water by 1°F was the same as the energy from a 772-pound weight falling one foot.

Understanding this conversion process lays the foundational thought that energy doesn’t disappear; it changes forms. This principle is essential for explaining phenomena across various scientific disciplines, from thermodynamics to modern energy systems.

Specific Heat of Water

Specific heat is a property that shows how much heat energy is required to change the temperature of a substance. Water is a remarkable substance due to its high specific heat capacity.

• For water, it takes 1 calorie of heat energy to raise the temperature of 1 gram by 1°C.
• To raise 1 gram by 1 degree Fahrenheit requires slightly less, about 0.9 calories, due to the conversion factor between Celsius and Fahrenheit.
• In Joule’s context, 1 pound of water, which equals 454 grams, would need much more energy to see the same temperature change.

The specific heat capacity of water helps in comparing the work done, as shown in Joule's calculations. It highlights how energy conversion results in temperature changes, illustrating why the nature of specific heat is so critical to understanding how heat energy impacts different materials. Water's high specific heat makes it an excellent medium for thermal regulation in many scientific and natural processes.