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1. Why is Cp always greater than Cv?

Let 1 mole of an ideal gas be heated so that its temperature arises by a certain amount.  If the volume is allowed to be constant, no work will be done.  Therefore heat is needed only to raise the temperature and nothing else.  So less amount of heat (Q) will be required for the purpose.  Then according to the relation,

the value of C, i.e. Cv will be less.


However, if pressure is allowed to be constant, the volume has to be increased.  So the system would have to do work also and it has to increase the temperature also by the same amount as before. So, more amount of heat (Q) will be required.  Then according to the same relation,



the value of C, i.e. Cp will be more.




2. Why is the latent heat of vaporization of water greater than the latent heat of fusion of water?

The latent heat of fusion and vaporization both involve the heat required to change the state of a substance without a change in temperature. In the case of the latent heat of fusion it is the heat required to change a substance from a solid (ice) to a liquid (water) or vice versa while the latent heat of vaporization from a liquid (water) to a gas (steam) or vice versa.

In solids, the molecules are very close together and the attraction between the molecules are great. This causes a substance to have a structure in which the molecules have little freedom to move, as you would see in the case of ice. In the case of a liquid, the molecules are closely spaced, though not as closely spaced as a solid, they have more freedom to move and the intermolecular forces are weaker that that of a solid. Thus a liquid can flow, unlike a solid. Now in a gas, the molecules are sufficiently far apart that there are little to no attractive forces. Because of this a gas can easily be compressed and take the shape of the container.

Now as you heat a solid turning it into a liquid, you increase the kinetic energy of its molecules, moving them further apart until the forces of attraction are reduced to allow it to flow freely. Keep in mind the forces of attraction still exists. Now as you heat a liquid, turning it into a gas, the kinetic energy of the molecules are increased to a point where there are no forces of attraction between the molecules.

The energy required to completely separate the molecules, moving from liquid to gas, is much greater that if you were just to reduce their separation, solid to liquid. Hence the reason why the latent heat of vaporization is greater that the latent heat of fusion.



3. It is well known that water expands when it freezes, which is why frozen pipes burst. This means that water can do work as it freezes. Where does the energy come from for this to happen? This is especially puzzling considering that energy is being removed from the water in order to freeze it.

The answer is in the question. When water freezes, it releases significant amounts of energy, called latent heat. If the water is in a pond, this energy flows into the surrounding air as heat. But if the water is trapped inside a copper pipe, some of this energy is used to burst the pipe so the water can expand. This means there is less energy available to flow into the surroundings in the form of heat.

The confusion perhaps arises because of the term "latent heat", which implies that the energy has to be lost in the form of heat and not in any other form. This is not the case



4. Why does heat and cold make things expand and contract? Also why do some metals expand more than others?

Recall that all materials are made up of atoms. At any temperature above absolute zero (-273 0C) the atoms will be moving. In a solid they will be vibrating in fixed positions, in a liquid thy will be jostling past each other and in a gas they will be whizzing past each other at very high speeds. When a material is heated, the kinetic energy of that material increases and it's atoms and molecules move about more. This means that each atom will take up more space due to it's movement so the material will expand. When it is cold the kinetic energy decreases, so the atoms take up less space and the material contracts.

Some metals expand more than others due to differences in the forces between the atoms / molecules. In metals such as iron the forces between the atoms are stronger so it is more difficult for the atoms to move around . In brass the forces are a little weaker so the atoms are free to move about more. These differences in contraction are used in a bimetallic strip, which is composed of a strip of brass laid along side strip of Iron. When the strip is heated the brass expands more than the iron so the strip beds. It is used in devices such as fire alarms and circuit breakers to either make or break contacts in an electric circuit.

The differences in expansion and contraction are even more visible in different states, again due to the amount of force holding the atoms together. A gas will expand the most as its atoms are free from each other so are free to increase in speed the most.






6. If temperature is 'The average kinetic energy of particles' (i.e. if you measure the temperature of a cup of water it is the average of all the water molecules in the cup), then how does one determine the temperature of a vacuum?

One doesn't determine the temperature of a vacuum. Just as 'nothingness' has no color, taste, smell, etc. it also has no temperature. That is because, as you point out in your question, there are no particles whose kinetic energy can be measured or averaged.

Only objects within a vacuum can have a temperature, and that temperature will depend on the balance of incoming and outgoing radiation. Electromagnetic radiation can travel through a vacuum, so objects in space of any temperature above the near absolute zero (0 Kelvin = about -273 0C.) temperature of cosmic background radiation (which is about 3 Kelvin) will radiate energy into space. Without another source of energy replacing that loss (a nearby Sun, for example) the object's temperature will decrease. That is why you read about 'the coldness of outer space'.



7. Since the sun is one giant ball of gas, what force holds its consistent shape and size? Why doesn't it expand and burn up quickly?

The Sun maintains its size and shape against the outward pressure of fusion energy by the force of gravity. In other words, its own weight keeps the Sun from growing larger.

It is the stable balance of outward gas pressure vs. the inward pull of gravity that determines the size of any star.

The predominantly spherical shape of all but the smallest astronomical bodies (asteroids, for example) is due to the radially symmetric nature of the gravitational force.



8. Why is it that when one is taking a hot shower, the shower curtain tends to be pulled inward, inside the shower (as opposed to being pushed outward)?

Hot air is less dense than usual air and therefore rises up. This takes effect in a shower where the hot water heats up the air on the inside of the curtain. This hot air rises upwards creating a very partial vacuum in the inside of the shower. This results in decrease in the pressure on the inside of the curtain as compared to the pressure on the outside of the curtain. This results in the curtain being 'pushed' inwards.










11. If you left the refrigerator door open, what would happen to the room temperature and why?

The room would get warmer! Think of a refrigerator as a device that transfers heat from inside a box to its surroundings. The room around a refrigerator is warmed as it receives the heat removed from inside the box.
If you leave the door open, heat is merely recycled from the room into the refrigerator, then back into the room, neutralizing the amount of heat entering the device and coming out of the device. But the motor of the mechanical pump used to remove the heat would also be releasing its share of heat to the room. So the overall effect is that the room would get hotter and hotter.







13. Will a black container of hot water lose heat faster or slower than a white container of hot water?

A black body is assumed to be a perfect radiator of heat.
A black container of water can be said to be closer to a black body than a white container. Kirchoff's laws of radiation make it evident that a BLACK BODY IS NOT ONLY A PERFECT ABSORBER BUT ALSO A PERFECT emitter of heat. Hence the black container will cool down faster.
Wear a black cotton shirt in summer, you'll sweat!
Wear a cotton (black) shirt in winter you'll freeze!



14. Books say that heat transfer in an adiabatic process is equal to 0. How can this be if there is a change in temperature?

You are probably making the common mistake among students by not realizing that heat and temperature are two completely different things.

Heat is a quantitative measurement of energy whereas temperature is a qualitative measurement which indicates the warmth or coldness of an object.

In an adiabatic process, there is no heat transfer to or from the system, and therefore

dQ = 0

or, dU + P dV = 0

or, dU = - P dV

Heat can not flow out of the system in an adiabatic process, but work can be performed on it from outside and it can also be allowed to do work.

When the system is allowed to do work, it requires energy, which it obtains at the cost of the internal energy it already possesses. So the total share of the internal energy decreases, thereby decreasing the temperature overall (Remember, no heat has been extracted out).


15. How can you boil a liquid without heating it? Why and how is this possible?

The boiling point of a liquid depends on both temperature and pressure. As pressure increases, so does the boiling temperature. Pressure cookers are used in cooking to raise the temperature at which liquids within will boil. Conversely, the lower atmospheric pressure on a mountain top makes it harder to get boiling water hot enough for good tea or coffee.

Boiling occurs when a liquid's molecules have enough energy to break free from surrounding molecules. Think of higher pressure as making that escape more difficult by offering a counteracting force.

Water boils under normal atmospheric pressure at 212F (100 C). Imagine it at 221 F (105 C) but NOT boiling in a pressurized container. If the pressure is quickly reduced, the 221 F (105 C) water at normal pressure will now boil.

For another example, put water at room temperature into a vacuum chamber and begin removing the air. Eventually, the boiling temperature will fall below the water temperature and boiling will begin without heating.


16. Considering only temperature and disrespecting the rest, would I feel cold or hot with my hand in the vacuum?

Your hand 'feels' hot or cold when heat is transferred to or from it, respectively. There are only 3 ways that heat can be transferred--by conduction, convection, or radiation. Only the third (radiation) can take place in a vacuum. That is how the Sun's energy is able to reach the Earth.

What your hand feels in a vacuum depends on the radiation falling upon it. For extreme examples, the vacuum a few thousand miles from the Sun's surface would feel very warm as it absorbs highly energetic photons. The vacuum in interstellar space, however, contains only background radiation close to absolute zero (-273oC.). In that situation, your hand at body temperature loses more energy than it gains, and would feel cold.

Any material object at a temperature above absolute zero radiates energy. In the case of a vacuum chamber, the temperature of the chamber walls will determine the radiation environment. If they are above the temperature of your hand, your hand will absorb the radiation and feel warmth. If they are below your hand's temperature, your hand will feel coldness.



17. Is it possible to make a perfect vacuum?

Practically, it is impossible to make a perfect vacuum. A perfect vacuum is defined as a region in space without any particles.

The problem is that to maintain a vacuum in a region you have to shield it from the environment. It is not difficult to make a container that would prevent atoms from entering the region.

The first problem is that the container itself will radiate photons (which in turn can create electron positron pairs in the vacuum) if it is not kept at a temperature of 0 K. Note that a perfect vacuum has by definition a temperature of 0 K. reaching 0 K is practically impossible.

The second problem is that there are weakly interacting particles that could enter the region. No matter how thick the walls of the container are, there is always a finite probability that, say, a neutrino would enter the region.


18. A student was messing around with the Bunsen burner when he noticed the following - He had put a wire gauze on top of the burner before turning the gas on. When he used the lighter on the bottom portion i.e. below the wire gauze, a flame was only visible at that portion but not above the wire gauze. When he used the lighter on the portion above the wire gauze, the flame only appeared on the top portion but not the bottom portion! Why?

What a great observation! Most people have never even thought of this, though they observe it often.

Well, what could it be about the wire gauze that might explain this wonderful event? Wire is a great heat sink (because of its high conductivity)! So, think about why a gas burns. It has to have enough thermal energy to begin the chemical reaction. If you light the gas below the gauze the lighter provides the energy to begin the burning. But the gauze takes away the thermal energy, because of the conductivity, which would otherwise be there to ignite the gas above the gauze. If you light the gas above the gauze the same thing happens. Either way, the gauze, acting as a heat sink, removes the thermal energy from the system so that the temperature above or below it is not sufficient to ignite the gas.


19. When one looks at a bedside light which is pointing upwards, one sees particles of dust near the light being sucked downwards towards the bulb. Convection should cause the opposite to happen, so what is going on?

I have often observed the phenomenon you mention. The reason is simple. The dust particles do travel upwards, but only up a thin "chimney" of rising air, heated strongly and rapidly by the bulb, which would be at several hundred degrees Celsius. The dust moves so quickly up this chimney that it is actually quite difficult to see. The reason it moves so quickly is the relative narrowness of the chimney compared to the powerful heating supplied by the bulb.

The dust you see moving downwards is coming from the cooler air away from the bulb. The shape of the convection current is rather like that of a bagel: the air is rising through the hole in the middle and so it has to move downwards around the outside in order to supply more air to replace that which has been heated and is rising. Because the outside edge of this bagel is larger than the inside edge, the air does not have to move as quickly to keep up, and so it seems to drift serenely downwards towards the bulb. The dust which appears to float straight down onto the surface of the bulb is actually behind the bulb, but because the dust particles are so small, it is hard to judge distance. The dust between you and the bulb and to the sides of it is not visible, as it reflects light towards the source, and not towards you.


20. I have always believed that in hot, sunny weather it is best to wear white or light-colored clothing because this reflects the heat. But a friend insists that the opposite is true and that black clothing is better because it helps to radiate heat from the body. Who is right? Or is a combination of the two--black on the inside and white outside--the best option?

You are right and your friend is wrong. Although it is true that dark objects radiate heat more effectively than light-coloured ones, the amount of heat radiated from a body is proportional to its absolute temperature to the power of four. This means that a human body does not lose much heat to the environment by radiative transfer. Most of the heat loss is by conduction, convection and (through sweating) evaporative cooling.

However, all of the energy from the Sun is transferred radiatively, so wearing black or dark clothes will help you to absorb it much more efficiently (and so make you very hot), while making only a minute difference to your ability to lose heat to the environment.


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