Why Temperature Depends on Internal Energy, Not Pressure/Volume

In summary, the temperature of an ideal gas is solely dependent on its internal energy. However, for a real gas, the temperature can also depend on other variables such as pressure or volume, depending on the system setup. In general, any two out of the variables (temperature, pressure, volume) are considered independent, while other quantities like internal energy are expressed in terms of them. For an ideal gas, the internal energy only depends on temperature, but for a real gas, this is not always the case.
  • #1
Tahmeed
81
4
Why temparature is only dependent on internal energy of something, say an ideal gas.
 
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  • #2
Which other dependency would you expect?
What is "porv"? Pressure or volume? It can depend on those, depending on the setup.
 
  • #3
I think he means pressure or volume. Like mfb said, it can depend on these variables, depending on the system. Usually, for a gas, any two variables out of (T, p, V) are considered as the independent variables, and other quantities, such as internal energy, or compressibility, etc., are expressed in terms of these independent variables. The internal energy depends only on temperature, for an ideal gas. This is not true for a real gas.
 

Related to Why Temperature Depends on Internal Energy, Not Pressure/Volume

1. Why does temperature depend on internal energy and not pressure/volume?

The temperature of a substance is a measure of the average kinetic energy of its particles. This kinetic energy is directly related to the internal energy of the substance, which includes all forms of energy such as chemical, nuclear, and thermal energy. Pressure and volume, on the other hand, only affect the spacing and movement of particles, not their actual kinetic energy. Therefore, temperature is dependent on internal energy, not pressure or volume.

2. How does the relationship between temperature and internal energy explain the behavior of gases?

In gases, the particles are in constant, random motion, colliding with each other and the walls of the container. As the temperature increases, the average kinetic energy of the particles also increases, causing them to move faster and collide more frequently. This increased internal energy leads to a higher temperature, and vice versa. Additionally, the temperature of a gas can change without a change in its pressure or volume, further demonstrating the dependence on internal energy.

3. Can changes in pressure or volume affect the temperature of a substance?

Yes, changes in pressure or volume can indirectly affect the temperature of a substance. For example, when a gas is compressed, its volume decreases, causing the particles to have less space to move around in. This results in a higher frequency of collisions, which increases the kinetic energy and temperature. However, the direct relationship is between temperature and internal energy, not pressure or volume.

4. How does the first law of thermodynamics support the relationship between temperature and internal energy?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. This law supports the relationship between temperature and internal energy because a change in temperature is a result of a transfer or conversion of internal energy. This further reinforces the idea that temperature is dependent on internal energy, rather than pressure or volume.

5. Are there any exceptions to the relationship between temperature and internal energy?

There are some rare cases where the relationship between temperature and internal energy may not hold true. One example is when a substance undergoes a phase change, such as melting or boiling, where the energy added or removed is used to break or form intermolecular bonds rather than increase the kinetic energy of particles. However, in most cases, the relationship between temperature and internal energy remains consistent.

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