## anonymous one year ago 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

1. anonymous

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2. anonymous

at constant T

3. IrishBoy123

$P(V-b)=RT$ $P=\frac{RT}{(V-b)}$ can you go from here?

4. IrishBoy123

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?

5. anonymous

Will they be canceled?

6. IrishBoy123

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

7. IrishBoy123

or do this first $y=\frac{a.b}{(x-c)}$ what is dy/dx, if a,b,c are constants

8. anonymous

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

9. IrishBoy123

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