Question

The two key features of an ideal gas are:

a) ( U ) depends only on ( n ) and ( T ), not ( V )
b) The ( V ) dependence of ( S ) is given by a term ( nK ln(V) ) for a gas that obeys (a) but has some excluded volume, so ( S ) goes as _____, with ( B )

c) ( U ) depends on ( V ) and ( T ), not ( n )
d) The ( P ) dependence of ( S ) is given by a term ( nRT/V ) for a gas that obeys (a) but has some included volume, so ( S ) goes as ( AV ), with ( A )

Answer 1

Ideal gases are characterized by the internal energy depending only on the number of moles and temperature, and the entropy depending on the gas volume. For an ideal gas, these relationships are described by the ideal gas law, PV = nRT. Real gases with excluded volume require corrections to this model, such as the van der Waals equation.

Step-by-step explanation:

The two key features of an ideal gas are: (a) The internal energy (U) depends only on the number of moles (n) and temperature (T), not on volume (V), (b) The volume (V) dependence of entropy (S) is given by a term (nK ln(V)) for an ideal gas, but for a gas that has some excluded volume due to particle size, the entropy (S) would depend on the corrected volume (V - nb), where b is a constant representing the excluded volume per mole of gas. This correction is part of the van der Waals equation, which accounts for real gas behavior. For an ideal gas, the internal energy (U) is independent of volume, as ideal gas particles are considered to be point particles with no volume and do not interact with each other. The entropy (S) of an ideal gas increases with volume due to increased dispersal of particles, which is quantified as an nK ln(V) dependence in an ideal system. The ideal gas law, PV = nRT, relates the pressure (P), volume (V), and temperature (T) of a gas, where R is the gas constant and n is the number of moles.