Question

The internal energy of nmoles of an ideal gas depends on a. one state variable T.

b. two state variables T and V.
c. two state variables T and P.

Answer 1

Correct option a. one state variable T.

Step-by-step explanation:

In the case of an ideal gas it is shown that internal energy depends exclusively on temperature, since in an ideal gas any interaction between the molecules or atoms that constitute it is neglected, so that internal energy is only kinetic energy, which depends Only of the temperature. This fact is known as Joule's law.

The internal energy variation of an ideal gas (monoatomic or diatomic) between two states A and B is calculated by the expression:

ΔUAB = n × Cv × (TB - TA)

Where n is the number of moles and Cv the molar heat capacity at constant volume. Temperatures must be expressed in Kelvin.

An ideal gas will suffer the same variation in internal energy (ΔUAB) as long as its initial temperature is TA and its final temperature TB, according to Joule's Law, whatever the type of process performed.