# I Why is internal energy not a function of pressure?

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1. Feb 12, 2018

I'm reading a book on thermal physics and the author says this:

"In general, the internal energy will be a function of temperature and volume, so that we can write $$U =U(T,V)$$"

How do we know this intuitively and how do we know that internal energy is not a function of pressure as well?

2. Feb 12, 2018

### BvU

3. Feb 12, 2018

### Staff: Mentor

The equation of state of a substance (e.g., the ideal gas law) specifies the relationship between its temperature T, volume V, and pressure P. Once any two of these are specified, the third one is determined, and its thermodynamic state is established. In your book, the author chose to use T and V. But, the author could equally well have chosen T and P (provided he was referring to the internal energy per unit mass).

4. Feb 12, 2018

### rcgldr

Isn't the internal energy also a function of the amount of mass (could be expressed as density since volume is a parameter).

5. Feb 12, 2018

### Staff: Mentor

Internal energy is an extensive property, and thereby depends on the amount of mass (i.e., is proportional to the amount of mass). Density, of course, is the inverse of specific volume. So, internal energy per unit mass u is a function of T and P, P and v, or T and v, where v is the specific volume.

6. Feb 12, 2018

### rcgldr

So is big U an energy value or an energy per unit mass (or like pressure, an energy per unit volume) value ? From the wiki article, I got the impression it was an energy value.

7. Feb 12, 2018

### Staff: Mentor

Usually, upper case letters are used for the extensive properties such as internal energy and volume (U and V), and lower case letters are used for the intensive versions (i.e., extensive property per unit mass or per mole) specific internal energy and specific volume (u and v). However, this is not always done, and there is often ambiguity. Often, the context reveals which is being used.