Zipper has N links: each link has a state in which it is closed with energy 0 and a state in which it is open with energy ε. We require, however, that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1, 2 . . . s – 1) are already open.
(a) Show that the partition function can be summed in the form
Z = 1 – exp [–(N + 1)ε/τ] / 1 – exp (–ε/τ)
(b) In the limit ε >> τ, find the average number of open links. The model is very simplified model of the unwinding of two-stranded DNA molecules.
A zip-lock plastic sandwich bag filled with water can act as a crude converging lens in air. If the bag is filled with air and placed under water, is the effective lens converging or diverging?
Zincselenide has a band gap of 2.58 eV. Over what range of wavelengths of visible light is it transparent?
Zinc has an HCP crystal structure, a c/a ratio of 1.856, and a density of 7.13 g/cm3. Compute the atomic radius for Zn.
Zimmerman Clothiers manufactures womenâs business suits. The company uses a standard cost accounting system. In March 2014, 15,700 suits were made. The following standard and actual cost data applied to the month of March when normal capacity was 20,000 direct labor hours. All materials purchased were used in production.
Overhead is applied on the basis of direct labor hours. At normal capacity, budgeted fixed overhead costs were $125,000, and budgeted variable overhead costs were $63,000.
(a) Compute the total, price, and quantity variances for (1) materials and (2) labor.
(b) Compute the total overhead variance.
(c) Which of the materials and labor variances should be investigated if management considers a variance of more than 5% from standard to besignificant?
Zhong is considering three alternative investments of $10,000. Zhong is in the 25% marginal tax bracket for ordinary income and 15% for qualifying capital gains in all tax years. The selected investment will be sold at the end of five years. The alternatives are:
• A taxable corporate bond yielding 5.333% before tax and the interest reinvested at 5.333% before tax.
• A tax-favored bond that will have a maturity value of $12,200 (a 4% pretax rate of return).
• Land that will increase in value.
The gain on the land is classified and taxed as a long-term capital gain. The interest from the bonds is taxed as ordinary income: the interest from the corporate bond as it is earned annually, but that from the tax-favored bond is recognized only upon redemption.
How much must the land increase in value to yield a greater after-tax return than either of the bonds? Use the future value tables in Appendix F as needed for your calculations and comparisons.
Zheng Corporation had the following selected transactions in the month of March. The company adjusts its accounts monthly.
1. The company has an 14%, $12,040 note payable due in 1 year. Interest is payable the first of each month. It was last paid on March 1, and will be paid next on April 1.
2. At the end of March, the company earned $370 interest on its investments. The bank deposited this amount in Zheng’s bank account on April 1.
3. Zheng has five employees who each earn $240 a day. Salaries are normally paid on Fridays for work completed Monday through Friday of the same week. Salaries were last paid on Friday, March 27, and will be paid next on Friday, April 3.
4. At the end of March, the company owed the utility company $610 and the telephone company $300 for services received during the month. These bills were paid on April 10.
5. At the end of March, Zheng has earned $3,560 that it has not yet billed. It bills its clients for fees earned on April 1. On April 30, it collects $2,000 of this amount due.
(a) For each of the above situations, prepare the monthly adjusting journal entry required at March 31.
(b) Prepare any subsequent transaction entries that occur in the month of April.
Zhang Companyâs bank statement from Nguyen National Bank at August 31, 2014, shows the information below.
A summary of the Cash account in the ledger for August shows: balance, August 1, $10,959; receipts $50,050; disbursements $47,794; and balance, August 31, $13,215. Analysis reveals that the only reconciling items on the July 31 bank reconciliation were a deposit in transit for $3,200 and outstanding checks of $2,925. The deposit in transit was the first deposit recorded by the bank in August. In addition, you determine that there were two errors involving company checks drawn in August: (1) A check for $340 to a creditor on account that cleared the bank in August was journalized and posted for $430. (2) A salary check to an employee for $275 was recorded by the bank for $277.
(a) Prepare a bank reconciliation at August 31.
(b) Journalize the adjusting entries to be made by Zhang Company at August 31. Assume that interest on the note has not been accrued by thecompany.
Zero Time Oil Change has been in business for six months. The company pays $0.50 per quart for the oil it uses in servicing cars. Each job requires an average of 4 quarts of oil. The company estimates that in the next three months, it will service 240,288, and 360 cars.
1. Compute the cost of oil for each of the three months and the total cost for all three months.
2. Complete the following sentences by choosing the words that best describe the cost behavior at Zero Time Oil change:
a. Cost per unit (increased, decreased, remained constant).
b. Total variable cost per month (increased, decreased) as the quantity of oil used (increased,decreased).
Zero point lattice displacement and strain
(a) In the Debye approximation, show that the mean square displacement of an atom at absolute zero is R) = 3hw2D/8π2 pv3, where v is the velocity of sound. Start from the result (4.29) summed over the independent lattice modes: <R2> = (h/2pV) Σw–1. We have included a factor of ½ to go from mean square amplitude to mean square displacement.
(b) Show that Σw–1 and (R2) diverge for a one-dimensional lattice, but that the mean square strain is finite. Consider <(∂R/∂x)2> = ½ ΣK2u20 as the mean square strain, and show that it is equal to hw2DL/4MNv3 for a line of N atoms each of mass M, counting longitudinal modes only. The divergence of R2 is not significant for any physical measurement.