DQ 2

Question 1

For this question, treat 'y' as a function of the independent variable, 'x'. That is y = f(x) = y(x)

$$y(x) = \frac{ab}{x} \ a,b = constants \newline \nonumber \newline$$

$$\int_{x_1}^{x_2} y(x) dx = ? \nonumber$$

A.

$$-ab \left [ln\left(\frac{x_1}{x_2} \right) \right ] \nonumber$$

B.

$$ab \left [ln\left(\frac{x_2}{x_1} \right) \right] \nonumber$$

C.

$$ab \left [ln ( x_2 - x_1) \right] \nonumber$$

D.

$$ab \left [ln(x_2) - ln(x_1) \right] \nonumber$$

E.

$$ab \left [ ln(x_1 x_2) \right] \nonumber$$

F.

$$none of the above \nonumber$$

Question 2

Consider a fluid for which the relation between its pressure (P), volume(V), and temperature(T) is given by:

$$PV = nRT \nonumber$$

Consider a volume change from V1 to V2 while T is constant. R and n are constants.

$$\int_{V_1}^{V_2} p dV = ? \nonumber$$

A.

$$nRT \left [ ln(V_2) - ln(V_1) \right] \nonumber$$

B.

$$nRT \left [ ln ( V_2 - V_1) \right ] \nonumber$$

C.

$$nRT \left [ ln \left ( \frac{V_2}{V_1} \right) \right ] \nonumber$$

D.

$$ln(V_1) \nonumber$$

E.

$$none of the above \nonumber$$