Thermodynamics of a Perfect Thermal Insulator

• wintermute++
In summary, a perfect thermal insulator is a material that prevents the transfer of heat energy between two objects or regions. It works by limiting heat movement through thermal resistance and has properties such as low thermal conductivity, high thermal resistance, and low thermal diffusivity. While it is impossible for a material to be a perfect thermal insulator, certain materials, like aerogel and vacuum insulation panels, come close. These insulators have applications in building and spacecraft insulation, cryogenics, and energy-efficient products, and are crucial in maintaining thermal gradients and controlling heat loss in industrial processes.
wintermute++

Homework Statement

A sample of gas is contained in a cylinder-and-piston arrangement. It undergoes the change in state shown in the drawing. (The drawing shows the first state of the piston as and uncompressed gas, then the second state is compressed, possibly a liquid, with the piston having moved downward and decreasing the volume) a. Assume first that the cylinder and piston are perfect thermal insulators that do not allow heat to be transferred. What is the value of q for the state change? What is the sign of w for the state change? What can be said about the change in Internal Energy for the state change? b. Now assume that the cylinder and piston are made up of a thermal conductor such as a metal. During the state change the cylinder gets warmer to the touch. What is the sign of q for the state change in this case? Describe the difference in the state of the system at the end of the process in the two cases. What can you say about the relative values of changes in Internal Energy?

w = -PV
E = q + w

The Attempt at a Solution

a. Work is done on the system and is positive. This is the part that I'm stumbling over. If the cylinder is a perfect thermal insulator, then no transfer of heat can occur with the surroundings and since heat is the flow of energy from a hotter object to a cooler object, would q = 0 then or would it still be q < 0?

b. The change in state is exothermic with q being negative. If my above assumption is true and q = 0, then the relative changes in internal energy would be: the perfect thermal insulator has an overall increase in internal energy and the thermal conducting cylinder would have either a very small increase in internal energy or a decrease in internal energy.

Bah, thermodynamics are the only part of chemistry I struggle to get a firm grasp on. Please help!

Hello,

Thank you for your post. Let's go through your questions one by one:

a. If the cylinder is a perfect thermal insulator, then no heat transfer can occur with the surroundings. This means that q = 0, since there is no flow of heat between the system and its surroundings. The work done on the system is still positive, since the volume is decreasing and the pressure is constant. This means that the internal energy of the system is increasing, since E = q + w and q = 0. So, the change in internal energy for the state change is positive.

b. If the cylinder is made of a thermal conductor, then heat transfer can occur between the system and its surroundings. In this case, the change in state is exothermic (heat is being released from the system). This means that q < 0, since heat is flowing from the system to its surroundings. The work done on the system is still positive, since the volume is decreasing and the pressure is constant. This means that the internal energy of the system is decreasing, since E = q + w and q < 0. So, the change in internal energy for the state change is negative.

In summary, the main difference between the two cases is that in the first case (perfect thermal insulator), no heat transfer occurs and the internal energy of the system increases. In the second case (thermal conductor), heat transfer occurs and the internal energy of the system decreases.

I hope this helps clarify your understanding. Please let me know if you have any further questions.

1. What is a perfect thermal insulator?

A perfect thermal insulator is a material that does not allow the transfer of heat energy between two objects or regions. This means that it has a very low thermal conductivity and can effectively prevent heat from passing through it.

2. How does a perfect thermal insulator work?

A perfect thermal insulator works by limiting the movement of heat energy through a process called thermal resistance. This is achieved by reducing the material's thermal conductivity or by creating a barrier that prevents heat from passing through.

3. What are the properties of a perfect thermal insulator?

The main properties of a perfect thermal insulator are low thermal conductivity, high thermal resistance, and low thermal diffusivity. It also has a high melting point and is usually a poor conductor of electricity.

4. Can a material be a perfect thermal insulator?

No, it is impossible for a material to be a perfect thermal insulator. This is because all materials have some degree of thermal conductivity, even if it is very low. However, some materials can come close to being a perfect thermal insulator, such as aerogel or vacuum insulation panels.

5. What are the real-world applications of perfect thermal insulators?

Perfect thermal insulators have various applications, such as in building insulation, refrigeration systems, and spacecraft insulation. They are also used in cryogenic applications and in the production of energy-efficient products. Additionally, perfect thermal insulators are essential for maintaining thermal gradients and controlling heat loss in many industrial processes.

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