1. (33 points) A 1.00 kg iron (FE) horseshoe is taken from a furnace at 1100 0C and dropped into 4.00 kg of water (W) at exactly 90 0C. When the system comes to equilibrium, the final temperature of the water and horseshoe is Tf = 100 0C exactly.
    Thus, the horseshoe cools down from exactly 1100 degrees down to 100 0C, and 4.00 kg of water heats up to from 900C to
    100 0C. Assume also that mass m = 0.170 kg of the water vaporizes into steam at 100 0C.


(a) (10)What is the change in entropy of the metal?


(b) (10)What is the change in entropy of the water heating from 90 to 100 0C ?


(c) (10)What is the change in entropy of the water of mass m vaporizing into steam?

(d) (2) Is the total entropy change positive or negative? Prove your answer.


(e) (1)Based upon your answer in part (d), is the process reversible or irreversible? (Assume the metal and water form a closed system.)

Useful constants for this problem: Assume CW = 4.00x103 J/kg0C and LV = 2.00x106 J/kg for water , and CFE = 5.00x 102 J/kg0C for iron for the purposes of this problem.

 

2. (33 points) A point charge Q "floats" in a electric and gravitational field at a distance d directly above the top end of a charged rod. The mass of the point charge is m. The charge density of the rod is positive and has the value . The length of the rod is L.

(a) (3) Is Q positive or negative?
(b) (3) What direction does the electrical force on Q point?

(c) (27) What is the mass m of the point charge? Give your expression for the mass in terms of these and other relevant symbols. Show all work in the intermediate steps leading to the answer. Show all calculus steps !
 4B SP12 REFERENCE: FORCE AND FIELD ON AXIS OF A FROM A CHARGED ROD, BALANCING GRAVITY: 
QUIZ 1 #82; CH. 21 #89(NOT ASSIGNED)

 



3. EXTRA CREDIT (Ch. 24) ( 7 points)

A solid sphere of radius a has a total positive charge of Q.
Use symbols for the following derivations.
(a) (3 points) What is the magnitude E of the electric field at a distance 2a from the center?
(b) (4 points) What is the magnitude E of the electric field at a distance a/2 from the center?

4B SP12 REFERENCE: SOLID INSULATING SPHERE QUIZ 2, #23, #54