### Question

When carpet and a marble floor are at same room temperature, why does carpet feel warmer than a marble floor?

Your sense of an object's temperature actually depends on the direction of heat flow between it and your skin. When heat flows from the object to your hand, for example, the object feels warm to the touch. When heat flows from your hand to the object, it feels cool. You can confirm this by soaking one hand in warm water and the other in cold. Then, put each hand into room temperature water. The warm hand will make you think the water is cool, the cold hand will make you believe the water is warm.

Temperature difference between an object and your skin is one condition resulting in heat flow, but there are others.

Wind chill factor makes the same air temperature feel different to your skin because convection removes heat more quickly from you skin when air is moving over it. Another factor affecting the flow of heat is conductivity, or the ability of material to transfer heat efficiently. Some materials, like metals and marble, are good conductors and allow heat to flow easily from and to your skin. Other materials (called insulators), like the material in carpeting, are poor conductors and do not allow heat to flow very easily. So even when they are at the same temperature, a cold marble floor transfers heat quickly away from your feet, while a cold carpet prevents that flow from occuring as quickly. That makes the marble "feel" colder.
Answered by: Paul Walorski, B.A., Part-time physics instructor

This is a good question! How observant you are to notice that two objects at the same temperature feel differently. This is something that many people wonder about and few people really understand. The confusion lies mainly in the misunderstanding of the difference between temperature and heat.

Let's consider what temperature is. Temperature can be thought of as the average kinetic energy of the particles that make up a substance. The faster these tiny atomic or molecular particles move, the higher the temperature.

Let's consider what heat is. Heat is the transfer of energy from one location to another. You can think of heat as a verb. A word that means something is moving. What is moving? Energy is moving. To say the least, this is difficult to imagine!

Energy as heat always travels in the same direction: from an object that has more energy as heat to an object that has less energy as heat. In other words, energy as heat will travel from an object with a higher temperature to an object with a lower temperature.

When you touch something you have to remember that your finger has some energy as heat. If what you touch has less energy as heat than you it will feel cold. If the object has more energy as heat it will feel hot.

The reason for these different feelings is because you are either giving some of your body's energy as heat to the substance, so it feels cold. Or, the object is giving you some of its energy as heat to you so it feels hot.

Do you suppose that all objects are able to transfer energy as heat equally? Of course not!

You know that metals transfer energy as heat easily. This is why a metal cake pan in the oven cannot be touched with your bare hands. So much energy as heat will be transferred to your hand so quickly that your hand will burn.

However, that same hand can be put into the oven where the air is at the same temperature as the metal cake pan and not be burned unless you keep it there a very long time. This is because air does not transfer energy as heat nearly as well as metal does.

This works at the other end of the scale. If you touch a piece of metal that is below zero you cannot hold your hand there for long because the metal is taking so much energy as heat from your hand that you soon feel very uncomfortable.

However, you can tolerate air that is below zero for a much longer period of time. This is because, again, air does not transfer energy as heat very well.

As you might expect, there is a name for this property of matter. It is called 'specific heat'. If you go to your favorite search engine and type this term in to the search box you will find links to tables that will tell you the specific heats of many different substances.

If you look for the specific heat of carpet you will see that it is a very low number while the specific heat of marble is much higher. This means that carpet does not transfer energy as heat very well but marble transfers energy as heat very well indeed.

Since carpet does not transfer energy as heat very well it will not take very much energy as heat from you when it is at a lower temperature. Thus carpet at a low temperature will not feel very cold. But, marble does transfer energy as heat very well so it will take a lot of energy as heat from you quickly. Thus marble at a low temperature will feel very cold.

I hope this answer helps you to understand the very important difference between temperature and heat. If you keep being observant many more questions will come to you about this fascinating area of physics.
Answered by: Tom Young, B.S., Physics teacher at Whitehouse High School

How hotsomethings feels (other than its actual temperature) is dependant on its heat capacity and the rate at which heat is removed from the surface.

In this case, therelevantt way of looking at heat capacity is as the energy required to heat up a certain volume of material. Since temperature is just the average kinetic energy of atoms, the heat capacity per unit volume is dependant on the number of atoms per unit volume. Heat conduction is also closely related to the atom number-density of a material, but also depends on the structure and the freedom of the atoms to move within the material and pass on their energy to other atoms.

Marble, being a dense solid requires a lot of energy to pass from your body to warm up. It also has a reasonable rate of heat conduction, so the surface remains cold for some time when in contact with your body.

Carpet, on the other hand has a very small number density, because most of the volume is occupied by air. It therefore warms up very quickly to the temperature of your skin, at which point it is preventing further heat loss and feels warm.

In reality the carpet never reaches the temperature of your skin, because it is constantly being cooled by the replacement of warm air with cool air. So unlike marble, the main cooling process for carpet is not conduction, but convection.

### Science Quote

'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.'

Paul Dirac
(1902-1984)