anonymous
  • anonymous
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
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
at constant T
IrishBoy123
  • IrishBoy123
\[P(V-b)=RT\] \[P=\frac{RT}{(V-b)}\] can you go from here?

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IrishBoy123
  • 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?
anonymous
  • anonymous
Will they be canceled?
IrishBoy123
  • 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
IrishBoy123
  • IrishBoy123
or do this first \[y=\frac{a.b}{(x-c)}\] what is dy/dx, if a,b,c are constants
anonymous
  • anonymous
y' = ab/(x-c)^2 :)
IrishBoy123
  • 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

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