What is the physical reason for the increase of the chemical potential of a pure substance as the pressure is raised?

Investors are often interested in knowing how long it takes for a particular investment to double. A simple means for making this determination is the "rule of 70," which says: The doubling time of an investment with an annual interest rate r% compounded continuously is given by $d=\frac{70}{r}.$ a. For interest rate r, use the formula $B=P e^{r t}$ to find the doubling time for r = 4, 6, 9, 10, and 12. In each case, compare the value with the value obtained from the rule of 70. b. Some people prefer a "rule of 72" and others use a "rule of 69." Test these alternative rules as in part (a), and write a paragraph on which rule you would prefer to use.

Desert sand is very hot in the day and very cool at night. What does this tell you about its specific heat capacity?

Given $L_n$ or $R_n$ as indicated, express their limits as $n \rightarrow \infty$ as definite integrals, identifying the correct intervals.

$$R_{n}=\frac{1}{n} \sum_{i=1}^{n} \frac{i}{n}$$

Give two ways to write algebraic expression $x+0.5$ in words.

(a) By how much does the chemical potential of copper change when the pressure exerted on a sample is increased from 100 kPa to 10 MPa? Take the mass density of copper to be $8960\ \mathrm{kg}\ \mathrm{m}^{-3}.$ (b) By how much does the chemical potential of benzene change when the pressure exerted on a sample is increased from 100 kPa to 10 MPa? Take the mass density of benzene to be $0.8765\ \mathrm{g}\ \mathrm{cm}^{-3}.$

Find the fourth partial sum $S_4$ of the given series. $\sum_{n=1}^{\infty} \frac{1}{2^{n}}$

Describe how the concept of chemical potential unifies the discussion of phase equilibria.

Which equation has the same solution as z - 9 = 3? (A) z - 4 = 16 (B)

$$\frac { 1 } { 2 } z = 7$$

(C) z + 15 = 27 (D) 5z = 45

Grammar The forms of the ver jugar are: The preposition con becomes... to mean " with me" and... to mean"with you".

Sketch each parabola. Label the x-intercepts and vertex.

$$\begin{array} { l } { \text { a) } y = ( x - 6 ) ( x - 2 ) } \\ { \text { b) } y = - ( x + 3 ) ( x + 7 ) } \\ { \text { c) } y = 2 ( x - 3 ) ( x + 2 ) } \\ { \text { d) } y = - 2 ( x - 4 ) ( x + 2 ) } \end{array}$$

Find the derivative of the given function. $y=\frac{2-x^{2}}{3 x^{2}+1}$

Why does the chemical potential change with pressure even if the system is incompressible (i.e remains at the same volume when pressure is applied)?

Why does the chemical potential change with pressure even if the system is incompressible (that is, remains at the same volume when pressure is applied)?