The reasons of popularity of Sir Arthur Conan Doyle’s stories about the fictional detective Sherlock Holmes

On the 6th of February 2004, our Physics class was invited to take a tour of the skiing facility at Xscape in Milton Keynes. The visit gave me a good insight into different areas of Physics that were seen at the skiing complex. We learnt a lot about the cooling system, how it works, and areas of energy loss which could be harnessed instead of lost. We were given a tour as well as a brief talk about Xscape by Mr. Shears.

Section 1: Aspects of Physics Observed

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1.1

I observed the operation of drag lifts at Xscape which took skiers back up the ski slope. Each drag lift consisted of 16 hangers onto which the skiers would sit on when going up the ski slope. The cable used to carry all 16 skiers needs to be able to support the 16 skiers by withstanding high degrees of tension. This tension acts on the cable in opposite directions, but these tensions will not equal each other. This is explained below:

I am going to focus on the tensions in the cable for one skier sitting on a hanger being pulled up the ski slope. We were told by Mr. Shears that the cable to the top of the slope is at an angle of about 22� to the horizontal and the cable down to the bottom of the slope was at about 20�. We can find the tensions in the cable by resolving forces acting horizontally and vertically on the cable.

We know that the horizontal component of T1 and T2 must be equal to each other in opposite directions:

T1cos22 = T2cos20

T2 = T1(cos22�cos20) (1)

The vertical component of T1 that acts upwards is equal to the weight of the skier, mg, where m is the mass of the skier and g is the force acting downwards due to gravity plus the vertical component of T2, also acting downwards:

Mass, m=75kg

Gravity=9.81Nkg-1

T1sin22 = mg + T2sin20 (2)

We can substitute equation (1) into equation (2) to give:

T1sin22 = mg + T1(cos22 � cos20)sin20

T1 = mg � [(sin22) – sin20(cos22�cos20)] = 1.98X104N

We can substitute T1 into equation (1) to give:

T2 = T1(cos22�cos20) = 1.95X104N

From these calculations, we can see that the tension acting in the opposite direction is not the same. A cable that is able to withstand a tension of about 20000N acting on it in opposite directions should be used for the drag lifts. We can also see that T1 and T2 cannot be the same because the two angles made by the cable to the horizontal are not equal and therefore one will be greater than the other.

1.2

The cooling system at Xscape effectively uses almost the same cooling process in a fridge freezer but here it is of an industrial scale. The main element of physics that occurs through this system is energy changes. The snow is cooled using a network of pipes that run underneath the snow box. Flowing through the pipes is glycol at temperatures of between -6�C to -14�C. The system works by compressing low temperature glycol gas using electricity. As the glycol compresses work is done on the gas and its volume reduces. There is no heat transfer in this closed system which leads to an increase in the internal energy of the glycol and subsequently increases its temperature, known as adiabatic compression. The liquid then passes through a condenser where the heat is removed as heat energy radiates from the pipes and is taken away by fans and blown outside.

Future Developments

This part of the process loses a large amount of heat energy which could have been distributed through the use of ducts and fans to other areas of the Xscape complex, such as to the restaurants. Using this heat energy will reduce the complex’s existing heating bill resulting in the business being more energy efficient. In the short term, the introduction of large fans and ducts to the complex may prove expensive, but in the longer term the savings made in heating bills will be able to cover the cost of introducing the ducts and fans.

The thermal energy given off could be used to heat up the water that is supplied to the complex. Rather than using boilers that use electricity, the business could save costs by directing the thermal radiation to a water tank. This process of heating water could be improved by using a conductive material for the water tank which has a high thermal conductivity, for example copper which is 400Wm-1k-1.

Section 2: Purpose of each Aspect

2.1

The operators of the drag lifts need to be sure that the cable they use will be able to cope with these tensions in order to make sure the facility is safe to use. Therefore the aspect of physics concerned with forces was used to choose a suitable material for the cable so that it would be able to cope with the tensions involved. By calculating the theoretical tensions, the operators are able to order a suitable cable from suppliers by quoting the tensions that it should be able to cope with. Thus ensuring that the cable being used is the right one for the job and also that the firm is purchasing the right one rather than one which is more costly and is designed to carry more load.

These lifts must be serviced regularly in order to prevent failure. This could result in the closure of the snow dome as customers cannot travel back up the slope.

A major disadvantage to the company is the large running costs of the drag lifts as they are running constantly from opening to closing time.

2.2

Once past the condenser the liquid glycol passes through an expansion device where its pressure is suddenly lowered and as a result some of the glycol evaporates, forming vapour. This change in state has a cooling effect. The cool vapour and liquid pass through a network of pipes arranged underneath the ice and snow in the ice box. Here heat energy is transferred from the ice box to the liquid glycol, since heat flows from warm bodies to colder bodies, resulting in the glycol changing back into low pressure, cooler gas. Therefore the purpose of this aspect of physics is to maintain a cool temperature within the ice box, between the temperatures stated earlier so the snow does not melt and nor does it form into ice.

It is essential to monitor the temperature of the glycol that flows under the snow box because if its temperature rises above that of the snow box, then heat will be absorbed by the cooler snow and ice resulting in the snow melting.

Detailed account of the main aspect of Physics

Energy Changes that occur during the process

Internal energy:

During the compression of cool, low pressure glycol, it is given more internal energy. That is according to the first law of thermodynamics, when the piston compresses a gas, the speed at which glycol being reflected from the piston will be greater than their initial speed. Therefore after being reflected from the piston, the molecules of glycol will receive an additional energy which will be redistributed over time between all molecules of gas because of their own collisions. The result is an increase in kinetic energy.

Thermal radiation:

As the hot liquid glycol passes through the condenser, the vibrating and spinning molecules in glycol give off electromagnetic radiation which is absorbed by the molecules in the colder air outside resulting in these air molecules moving faster. Thus, the glycol loses energy and cools until it is at the same temperature as the air outside.

Adiabatic expansion:

During adiabatic expansion of glycol liquid in the expansion device, it does positive work which is the opposite of work done on it. Therefore the work done on the glycol is negative resulting in its internal energy reducing and thus also its temperature. This is a result of rapid adiabatic expansion of glycol which gives the glycol negligible time to take in heat from its surroundings so no heat is supplied to it and the energy needed to do work by the molecules is taken from the liquid’s internal energy. As their has been a rapid reduction in pressure, glycol molecules have been forced to travel a greater distance resulting in them gaining more potential energy due to an increase in the separation between the molecules while greatly reducing kinetic energy. As a result, at the surface, some of the faster upward moving molecules do not need as much energy to overcome the attractions from the other glycol molecules and so they escape from the liquid. As these faster molecules have gone, the kinetic energy of those left behind is further reduced resulting in the temperature of the liquid falling.

At Xscape, 20 tonnes of snow is made during one night from 12.30am to 8.00am. The specific heat capacity of ice is 2093Jkg-1 �C-1 . From these values it is possible to calculate the energy removed from the ice box by the flow of glycol through the network of pipes to cool the ice and snow from -6�C to -14�C at Xscape:

?E= mc??

= 20000kg X 2093 X 8�C

= 334880kJ

This shows that a large amount of energy is required by the cooling system and also a substantial amount of this energy is also wasted through the thermal radiation of liquid glycol to the air outside. Heat is absorbed by the cold liquid glycol, but with a slight temperature rise. This is because the heat energy input from the ice is being used to overcome the attractions between the particles as the liquid glycol changes from liquid to gaseous state.

Limitations of the cooling system

The cooling system is inefficient because there is a large wastage of energy in the form of heat. As the low temperature glycol gas is compressed by the compressor, it becomes a relatively highly pressurized, high temperature vapour. This vapour is cooled in a condenser where heat is transferred from the condenser to the cooler outside. The cooling system does not harness this wasted energy back into the process and therefore is unable to increase its efficiency.

Compacted snow and ice is removed from the ski slope every three days and as a result, the ski slope has to be closed for twelve hours during which the snow is replenished. As a result of this, Xscape is limited to the amount of money they can make during these periods as it is shut for a longer period of time.

Strengths of the System

The cooling systems provides a constant flow of cooled glycol through a network of pipes which keeps the snow and ice between the respected temperatures of -6�C to -14�C so that the snow does not turn to ice or turn to water. The system is not vulnerable to cracked or broken pipes situated under the snow box as it is possible to close off one section of piping and cordon off that slope area while the piping is repaired. Therefore Xscape is capable of running during a broken glycol pipe and so the business will not lose business.

Other Uses

Cooling systems are used in cars to cool the engine. Engine coolant that is used contains glycol which in the same way as at Xscape is pumped around the car engine. The liquid absorbs thermal energy given off from the engine. As stated earlier, cooling systems are used in fridge freezers in almost an identical way.

I enjoyed my visit to Xscape and was most fascinated with the varying aspects of physics concerning the cooling and also the making of snow.

Bibliography

Internet:

Specific heat capacity of ice – http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Thermal/HeatCapTable.html

Books:

AS Salters Horners Advanced Physics – used to help me with calculating tensions in a wire and format of drawing figure 1 and 2.

Oxford Revision Guides AS & A Level Physics – theory being thermodynamics and adiabatic expansion

Temperature, it turns out, is directly proportional to the kinetic energy of

the gas molecules. A change in temperature means that energy is being

transferred, one way or another, between the molecules’ kinetic energy and

some other store. In compression or expansion of a gas, that “other store”

is the “intermolecular” potential energy between different gas molecules

vaporization

change of a liquid or solid substance to a gas or vapor. There is fundamentally no difference between the terms gas and vapor, but gas is used commonly to describe a substance that appears in the gaseous state under standard conditions of pressure and temperature, and vapor to describe the gaseous state of a substance that appears ordinarily as a liquid or solid. Although most substances undergo changes of state in the order of solid to liquid to gas as the temperature is raised, a few change directly from solid to gas in a process known as sublimation.

The Boiling Point and Latent Heat of Vaporization

When heat is added to a liquid at its boiling point, with the pressure kept constant, the molecules of the liquid acquire enough energy to overcome the intermolecular forces that bind them together in the liquid state, and they escape as individual molecules of vapor until the vaporization is complete. Vaporization at the boiling point is known simply as boiling. The temperature of a boiling liquid remains constant until all of the liquid has been converted to a gas.

For each substance a certain specific amount of heat must be supplied to vaporize a given quantity of the substance. This amount of heat is known as the latent heat of vaporization of the substance. The quantity of heat applied for each gram (or each molecule) undergoing the change in state depends on the substance itself. For example, the amount of heat necessary to change one gram of water to steam at its boiling point at one atmosphere of pressure, i.e., the heat of vaporization of water, is approximately 540 calories. Other substances require other amounts.

Evaporation and Vapor Pressure

Liquids can also change to gases at temperatures below their boiling points. Vaporization of a liquid below its boiling point is called evaporation, which occurs at any temperature when the surface of a liquid is exposed in an unconfined space. When, however, the surface is exposed in a confined space and the liquid is in excess of that needed to saturate the space with vapor, an equilibrium is quickly reached between the number of molecules of the substance going off from the surface and those returning to it. A change in temperature upsets this equilibrium; a rise in temperature, for example, increases the activity of the molecules at the surface and consequently increases the rate at which they fly off. When the temperature is maintained at the new point for a short time, a new equilibrium is soon established.

The pressure exerted by the vapor of a liquid in a confined space is called its vapor pressure. It differs for different substances at any given temperature, but each substance has a specific vapor pressure for each given temperature. At its boiling point the vapor pressure of a liquid is equal to atmospheric pressure. For example, the vapor pressure of water, measured in terms of the height of mercury in a barometer, is 4.58 mm at 0�C and 760 mm at 100�C (its boiling point).

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