The primary objective of the experiment is to design and implement an empirical study to quantify the conversion of thermal energy from mechanical energy to heat and verify the amount of energy conserved. The activity will likewise incorporate basic investigation of heat transfer and thermodynamics. Above all, the analysis will connect James Joule's theoretical concepts to the real world applications. One of the goals is to minimize errors and achieve plus or minus five percent of energy conservation.

## Introduction

### The First Law of Thermodynamics

The first law of thermodynamics expresses that energy can neither be created nor destroyed but instead it is only transformed. The objective of the experiment is to verify energy conservation through the accounting of the all the energy conversion within the control system. It implies that the internal increase in the quantity of energy will be compared to the loss of potential, work and kinetic energies within the system (Edwards & Recktenwald, 2010). The connection between thermal energy and mechanical energy referred to as Joules Constant and it is estimated to be 778.17 lbf - ft/Btu. It implies that moving 778.17 lbf through a 1ft distance requires one pound of water of one degree Celsius.

### Joules Constant

James P. Joules is recognized for having quantitatively established the First Law of Thermodynamics initially attempted by Lord Kelvin. Joules started studies on energy changes in 1843 with focus on the relationship between electricity and magnetism and later on the mechanical implications of heat. Joule's Constant = 778.17 lbf-ft/Btu

In these studies, Joules clarifies how he used a dropping to spin electric magnet immersed in water within a coil. The process warmed and resulted in an increase in temperature. He established that, by and large, to increase water temperature by 10F it required a mechanical power capable of lifting 838 lb. perpendicularly one foot above the ground. It is a +7.7 percentage difference from the value presently accepted as the Joule's constant. The scholar was less impressed with the outcome and planned another examination to establish the constant more precision. In the study, the focus was to achieve the same, measuring the heat absorbed in the rarefaction or condensation of atmospheric air (Balmer, 2011). The receiver and condensing pumps are submerged in an extensive amount of water. A comparison of the amount of energy required to condense the atmospheric air within the receiver, the constant 809 lbfft / Btu will be given by the heat generated.

The outcome was +4.0 percentage difference from the as of now acknowledged value. The physicist was again not satisfied, fulfilled, going ahead to publish another study that sought to study the mechanical heat equivalent. These empirical studies comprised of a paddled wheel spun with an already known velocity in water. The paddle's kinetic energy was absorbed by the surrounding water through friction and predictably changed over to heat energy. The study resulted in a Joule's constant of 772.692 lbf-ft/Btu, a figure almost the same as the presently accepted value with -0.7 percentage difference. The study was repeated but now with mercury replacing water, achieving a value of -0.4 percentage difference from what is currently accepted. More accurate and advanced testing equipment has resulted in the presently accepted value of 778.17 lbf-ft/Btu as the Joule's Constant.

## Objectives

The objective is to exhibit the transformation mechanical work to its equivalent heat energy

Further, the study will seek to determine the relationship between the traditional units of heat and work

## Theoretical Background

Energy is among the most basic quantities in the physical science. It can be found in various forms and transformed into different forms. In this study, the conversion of mechanical energy into its equivalent heat energy was demonstrated and the relationship between traditional units of heat and work determined experimentally. As per the work-energy hypothesis that takes after the law of motion by Isaac Newton, the temperature of a body increases when the body is worked on by a force. The energy appears as kinetic energy and potential energy in general, alth4ough it may appear as internal energy. For instance, when a pair of hands is rubbed against each other, the temperature of the surrounding area increases as work is converted to heat. It shows that when a force is applied to an object, it results in an increase in temperature, as work is transformed into heat and consequently the increase in temperature (Edwards, & Recktenwald, 2010). The same concept was applied in the empirical study as a metallic cylinder was propelled against a mechanical work resulting from friction. The schematic for the study is depicted in Figure 1.

A nylon code is swathed around a metallic cinder and an object with some weight attached at the end of the cord. The chamber is turned while inside the enfolded cord to create mechanical work. The mechanical work is varied through the turning of the handle of the crank against the frictional force acting between the cord and the metal surface. The objective is to maintain equilibrium between the bucket and the cord. Subsequently, the upward force associated with friction acting on the cord balances the gravitational force brought about by the weight of the hanging object.

Force = Mass x Gravitational Force

F = Mg, Equation (1)

M represents the mass of the suspended object while F represents the force the force the cord exerts on the cord. On the cylinder, the amount of work done by the force of friction for each rotation of the crank is computed as the force multiplied by the cylinder's circumference. When the crank is rotated N times and 'D' as the diameter of the barrel,

W = N * F * (pD)

W= N * Mg * (p D).

Therefore,

W = (p D M g) N, Equation (2).

N stands for the number of rotations for the crank, which does mechanical work against the force brought about the friction. The work resulting from the frictional force contributes to the internal energy and subsequently resulting in temperature increases within the cylinder. The theorem of work-energy is W = DE. Considering that mechanical work is applied in raising the cylinder's internal energy, as well as the temperature, W can be represented as (Work) W = A (temperature Change)

DT, W = ADT Equation (3),

where 'A' in the equation is a constant; The commonest approach to increase the temperature of an object is through the addition of heat energy. Heat is depicted as the energy exchanged between objects due to the temperature difference. The heating process is simply a process of addition of energy to the object. Quantitatively,

Q = mc DT, Equation (4)

In the fourth equation, it represents the amount of heat energy added to the object, with 'M', 'c' and DT being the object's mass, specific heat, and temperature change, respectively. The kilocalorie is the traditionally non-SI unit used generally for heat energy. The parameter 'A' can be considered as Joules (a measure of work) necessary in raising the temperature of water, is the gradient of Work versus Temperature graph.

Thus, when a system is warmed, the product of 'M' and 'c' is the quantity of heat, in kilocalories, necessary to raise the temperature of water by one degree Celsius. Both work and heat represent energy although generally they have been quantified using different units. Customarily, calorie has been used in the measurement of heat energy, where it has been conceived that a calorie of heat can increase the temperature of a gram of water at roughly fifteen degree Celsius by one degree Celsius. In this study, the equivalence between joules and calories will be determined.

In a series of experiments, James Joule in the 1840s exhibited the equivalence of work and heat in a similar fashion. The present study is a modernized adaptation of Joule's examination. By consistently applying force on a system (the metallic cylinder), the temperature difference was monitored. A graph of Work versus Temperature was plotted and the gradient of the line determined. The gradient was compared to the amount of 'Mc', and the cylinder's mass and the constant 'c' for aluminum metal checked. When gradient 'A' is the amount of work necessary to increase a gram of water by one degree Celsius, and 'Mc' is the amount of work necessary to increase the temperature of a gram of water by a unit of degree Celsius, then Joules per Kcal is the following ratio: A/Mc. It is a critical constant that establishes the relationship between work (Joules) and heat (Kcal).

## Apparatus

Mechanical equivalent device with Aluminum cylinder, axle, counter system, and crank

Bucket

Electrical meter

Nylon Cord

Paper towel pieces

Two electrical leads,

Weights

### Description of Apparatus

In the study, the experimental setup is demonstrated in Figure 1. The crank that is attached to the aluminum cylinder and fitted to the axle will do the mechanical work. A counter on the mechanical assembly recorded the number of rotations of the crank. The nylon cord was wrapped three times around the barrel, and the frictional force between the cylinder and the cord emanates through the sliding action of the cord relative to the cylindrical surface. One end of the rope hangs beneath the lab table, where it is joined to a container holding substantial weights. As opposed to pulling the rope around the chamber, the barrel is rotated inside the cord. The objective is to try to maintain the bucket and cord stationary while the bucket remains suspended a couple of centimeters directly above the ground surface. Subsequently, equilibrium of gravitational and frictional forces is created.

Figure SEQ Figure \* ARABIC 1: Mechanical Work Apparatus

## Methodology

From the second equation, mechanical work is computed as W = (p D M g) N. By tallying the number of rotations achieved by the crank, mechanical work can be determined. The thermistor is used for measuring the temperature of the aluminum cylinder while in motion. The approach is based on the notion that electrical resistance is proportionate to the temperature of materials. The thermistor is inserted in the aluminum chamber, and electrical contacts are attached to the two copper rings, which are evident at the base of the barrel. As the barrel slides onto the powerful axle, the rings are pressed against the copper contacts (Balmer, 2011). The multimeter measures thermistor's resistance through leads joined to the copper contacts. The graph of these parameters depicted the relationship between temperature and resistance. The SI unit of resistance, which acts against the mechanical work done, is the Ohm (). The temperature of the aluminum barrel was computed from the readings of resistance from the thermistor.

The contraption consists of a uniquely designed calorimeter installed in a wooden box (C) with a coating to prevent heat loss to the environment. A couple of vanes (V) are created within the interior walls of the calorimeter. An axle with various brass paddles, represented as P, act as a churner and pivoted at the lower section to facilitate the turning of the fixed vanes. Screws are used for attaching the spindle to the drum. The drum is rotated by the handle or alternatively using falling weights, W, which are strings passed through a pulley system all the way to the aluminum cylinder. Duo vertically stationed scales are situated vertically through the path of the weights.

## Procedure

The two weights were made to fall perpendicularly through a height that was recorded as 'h" in the table. Subsequently, on falling, the weights...

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