Question

the pressure (P) , temperature (T) and molar volume (V) of a gas is described by the following equation" P(V-b)=RT, where R and b are constant. Evaluate at quantity

Answer 1

at constant T

Answer 2

\[P(V-b)=RT\]
\[P=\frac{RT}{(V-b)}\]

can you go from here?

Answer 3

its like a normal deriv but with some funny symbols

so what would \(\frac{dP}{dV}\) be, if every other letter in the equation stood for a constant?

Answer 4

Will they be canceled?

Answer 5

treat the P and the V as the variables, as if it were P = P(V), and treat R,T & b as constants.

normal rules apply

Answer 6

or do this first

\[y=\frac{a.b}{(x-c)}\]

what is dy/dx, if a,b,c are constants

Answer 7

y' = ab/(x-c)^2 :)

Answer 8

y' = -ab/(x-c)^2

minus sign :p

so for
\[P=\frac{RT}{(V-b)}\]
you would typically use this kind of symbology in thermodynamics
\[ \frac{\partial P}{\partial V} \Big|_T =-\frac{RT}{(V-b)^2}\]
to drive home that fact that T is being held constant