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12 Nov 2019
question 2
2. Assume we have a function f r41 c where c is a constant, that relates variables z y, and Shortly you will find that where, for example, meas the partisi dertvat hve of s wila nspest to y whaie hoking s constart. Eqjua- tion (1) is known as the 'cyelic relation' and it is frequently used in engineering, physics, and thermodynamics in particular. (a) As an exaumple, consider the ideal gas law, po - kT, where pis the pressure, w is the container volume divided my the number of molecules, k is the Boltzmann constant, and T is the temperat ure in an absolute scale (Rankine or Kelvin). The variables in this expression are p, ty and T Demorstrate that the eyclic equation holds for the ileal gas law. In other words, show that Note that all three derivat ives in (2) are very reasonable caleulations to perform (b) Now consster Van der Waals equation of state given by (p# 4emb) mkT, where a and b are constants that account for the inter molecular at tractions, and the finite volume of the molecules, respectively Although equation (2) holds, you will note that the derivative , is actuallv very hard to calculate singe it reguires one to solve for p as a fumction of p and T,and this requires oue to solve a cubic equmtion Here is where the real utility of (2) comes forth rone were to solve for the term ( , from (2), one would find that Each of the partial derivatives on right hand side of (3) is relatively easy to calculate, thus allowing one o calculate the left hand side with minimal effort. Determine è p for Van der Walls equation of state in terms of the var iables p.v. T and the constants a, b. Be sure to simplify your results.
question 2
2. Assume we have a function f r41 c where c is a constant, that relates variables z y, and Shortly you will find that where, for example, meas the partisi dertvat hve of s wila nspest to y whaie hoking s constart. Eqjua- tion (1) is known as the 'cyelic relation' and it is frequently used in engineering, physics, and thermodynamics in particular. (a) As an exaumple, consider the ideal gas law, po - kT, where pis the pressure, w is the container volume divided my the number of molecules, k is the Boltzmann constant, and T is the temperat ure in an absolute scale (Rankine or Kelvin). The variables in this expression are p, ty and T Demorstrate that the eyclic equation holds for the ileal gas law. In other words, show that Note that all three derivat ives in (2) are very reasonable caleulations to perform (b) Now consster Van der Waals equation of state given by (p# 4emb) mkT, where a and b are constants that account for the inter molecular at tractions, and the finite volume of the molecules, respectively Although equation (2) holds, you will note that the derivative , is actuallv very hard to calculate singe it reguires one to solve for p as a fumction of p and T,and this requires oue to solve a cubic equmtion Here is where the real utility of (2) comes forth rone were to solve for the term ( , from (2), one would find that Each of the partial derivatives on right hand side of (3) is relatively easy to calculate, thus allowing one o calculate the left hand side with minimal effort. Determine è p for Van der Walls equation of state in terms of the var iables p.v. T and the constants a, b. Be sure to simplify your results.
Bunny GreenfelderLv2
8 Oct 2019