Answer:
the equation is
P*V = mRT.
The partial derivatives are:
For P = mRT/V.
[tex]dP/dV = -\frac{mRT}{V^2}[/tex]
[tex]dP/dT = \frac{mR}{V}[/tex]
now, if we take:
V = mRT/P
[tex]dV/dT = \frac{mR}{P}[/tex]
[tex]dV/dP = -\frac{mRT}{P^2} = (dP/dV)^{-1} = -\frac{V^2}{mRT}[/tex]
If we take T = PV/mR
[tex]dT/dP = \frac{V}{mR} = (dP/dT)^{-1}[/tex]
[tex]dT/dV = \frac{P}{mR} = (dV/dT)^{-1}[/tex]
Answer: Question for edmentum : Part D
Next, consider a scientific law known as the ideal gas law. This law deals with the relationship between temperature and pressure of a fixed mass of gas. The law states that the product of the pressure (P) and volume (V) is proportional to the temperature (T) of the mass of gas. The equation can be expressed this way, with k as a constant value:
PV = kT
Based on this equation, what are the two possible outcomes of heating up a certain mass of air?
Explanation: edmentum's sample Answer
The pressure of the gas or the volume of the gas will increase as the temperature increases. That’s because, according to the ideal gas law, pressure and volume are directly proportional to temperature. The value of k does not change.
