Final answer:
The ideal gas law relates the pressure, volume, temperature, and number of molecules of a gas. The constant k can be determined by rearranging the equation, and P can be written as a function of V and T.
Step-by-step explanation:
The ideal gas law, PV = NKT, relates the pressure, volume, temperature, and number of molecules of a gas.
(a) To determine the constant k, we need to rearrange the equation to isolate k. Dividing both sides of the equation by T will give us PV/T = NK:
k = (PV/T) / N
(b) To write P as a function of V and T, we need to rearrange the equation again. Dividing both sides of the equation by V and rearranging will give us:
P = NK / V
The level curves can be represented by setting P as a constant, denoted as c. Therefore, the level curves are represented by the equation:
V = NK / c