Name__________________________

PHYSICS 112, Chapter 19-21, Test 1

Instructions:

0. General Instructions: Put your books, notes, etc. on the floor. Leave at least one seat between the nearest student. Raise your hand if you have any questions, statements or concerns. Please do not converse with your neighbors until after the exam. If your calculator has memory, erase it before beginning the exam.

1. Do your work on the test paper provided. Additional paper will be provided as needed.

2. Mark your answers with units in the spaces provided. (Always, always, check your units!) Leave the problem you have chosen to omit, blank.

3. Leave your papers open. Put your name on each paper turned in, especially the answer sheet.

Equations:

Ideal gas law: pV = nRT

Coefficient of linear expansion: a = DL / (L DT)

Adiabatic exponent (polytropic index): g = C_p/C_v

Work done by ideal gas: W = òpdV

Internal Energy of an ideal gas: DE_int = Q - W = n C_vDT

Heat content of a solid or liquid: Q = CDT = cmDT or Lm

Heat content of a gas: Q = nC_vDT = nC_pDT (depending on p or V)

Specific heat of an ideal gas: C_p = C_v + R

Efficiency of an ideal heat engine: e = |W| / |Q_H| = (Q_H - Q_C) / Q_H £ (T_H - T_C) / T_H

Stirling’s approximation: ln n! = n ln (n) - n

Binomial theorem: n! / (n - m)! m!

Constants:

Avogadro’s Number: N_A = 6.02 x 10²³ / mole

Gas constant: R = 8.31 J/ mol ^. K

Specific heat of water: c = 4.19 kJ / kg ^.K

Specific heat of ice: c = 2.22 kJ / kg ^. K

Heat of freezing (fusion) of water: L_f = 333 kJ / kg

Heat of boiling (vaporization) of water: L_v = 2260 kJ/ kg

Pressure conversion: 1 atm = 1.01 x 10⁵ Pa

Volume conversion: 1 liter = 1000 cm³ = 0.001 m³

Celsius to Fahrenheit: ^oF = 9/5 ^oC + 32

Ideal Gas Laws (for p-V diagrams):

Constant Quantity Process Name Formulae_______________

p Isobaric Q=nC_pDT; W = pDV

T Isothermal Q = W = [_______]; DE_int=0

pVg, TVg^-1 Adiabatic Q = 0; W = DE_int

V Isochoric Q = DE_int = n C_vDT; W = 0

__________________________________________________________________

Name_______________________

ANSWER SHEET Multiple Choice

Problem 1 [5] _______________

1. _______________________ [6] _______________

2. _______________________ [7] _______________

Problem 2 [8] _______________

1. _______________________ [9] _______________

2. _______________________ [10] ______________

Problem 3 [11] ______________

1. _______________________ [12] ______________

2. _______________________ [13] ______________

Problem 4 [14] ______________

1. _______________________ [15] ______________

2. ________________________ [16] ______________

Do any 3 of the following 4 problems. (17 pts each)

[1] A 150 g copper bowl contains 220 g of water, both at 20.0 C. A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g of water being converted to steam. The final temperature of the system is 100 C. (a) how much heat was transferred to the water? (b) How much heat was transferred to the bowl? (c) What was the original temperature of the cylinder. (The specific heat of Copper is 386 J/kg-K)

[2] A weather balloon is loosely inflated with helium at a pressure of 1.0 atm (=760 torr) an temperature of 15C. The gas volume is 2.2 m³. At an elevation of 20,000 ft, the atmospheric pressure is down to 380 torr and the helium has expanded, being under no restraint from the confining bag. At this elevation the gas temperature is -48C. What is the gas volume now?

[3] A car engine delivers 8.2 kJ of work per cycle. (a) before tuneup the efficiency is 25%. Calculate, per cycle, the heat absorbed from the combustion of fuel and the energy lost by the engine. (b) After a tune-up, the efficiency is 31%. What are the new values of the quantities calculated in (a) when 8.2 kJ of work is delivered per cycle?

[4] Suppose you put 1000 pennies in a cup, shake the cup, and then toss the pennies onto the floor. (a) how many different head-tail arrangements (microstates) are possible for the 1000 pennies? (b) What is the probability of finding 500 heads? (c) What is the probability of finding only 100 heads?

Do all of the following Multiple Choice (4pts each)

[5] The following table gives the initial length, L, the change in temperature, DT, and the change in length, DL, of four rods. Rank the rods according to their coefficients of thermal expansion, greatest first. (Note the different temperature scales!)

Rod L DT DL_______

I 2 m 10^o C 0.4 mm

II 1 m 20^o F 0.4 mm

III 2 m 10^o F 0.8 mm

IV 4 m 5^o C 0.4 mm____

A) I, IV, III, II B) II, I, III, IV C) II, III, I, IV D) III, IV, I ,II E) IV, III, I, II

[6] Materials X, Y, and Z are solids that are at their melting temperatures. Material X requires 200 J to melt 4 kg. Material Y requires 300 J to melt 5 kg, and Material Z requires 400 J to melt 6 kg. Rank the materials according to their heats of fusion, greatest first.

A) X,Y,Z B) X,Z,Y C) Y,X,Z D) Y,Z,X E) Z,Y, X

[7] Aluminum has a specific heat of 900 J/kg-K, brass has a specific heat of 380 J/kg-K, and lead has a specific heat of 128 J/kg-K. If 1 kg of each material were heated to 100^oC in boiling water and placed on a block of paraffin wax, which would sink into the wax the furthest?

1. The lead, because it is the heaviest for its size.

2. The aluminum, because it stores the most heat.

3. The brass, because it conducts heat the best.

4. They would all be the same because they are at the same temperature.

5. Depends on the shape of the different weights.

[8] Let 1 kg of water at 100^oC be completely converted to steam also at 100^oC, while being held at constant volume. The work done by the water/steam system as it builds pressure is 100 kJ. What is the change in the internal energy of the system?

A) 0 kJ B) -100 kJ C) 2160 kJ D) 2260 kJ E) 2360 kJ

[9] The table gives the heat transfer Q into (+) or out of (-) an ideal gas and either the work, W_BY, done by the gas or the work, W_ON, done on the gas, all in joules. Rank the four situations in terms of the temperature change of the gas, most positive first, most negative last.

Situation Q W_BY W_ON

I -50 -50

II +35 +45

III -15 -40

IV +20 +40

1. I, II, IV, III B) IV, II, III, I C) IV, I, II, III D) I, III, IV, II E) III, IV, II, I

[10] Find the work involved in the following processes as described on a p-V diagram for one mole of a diatomic gas.

1000 ê. . . . . . . . . . . . . . . . . .

ê . .

Pressure (Pa) | . . (Straight line)

| . .

250 | . . . . . . . . . . . . . . . . . .

ë_____.____________.____

1 3 Volume in m³

1. 500 J B) 750 J C) 1250 J D) 2000 J

[11] Find the work involved in the following processes as described on a p-V diagram for one mole of a diatomic gas.

ê. . . . . . . . . . . . . . . . . .

ê . .

Pressure (Pa) | . . (Adiabatic curve)

| . .

| . . . . . . . . . . . . . . . . . .

ë_____.____________.____

1 3 Volume in m³

1. 225 J B) 1870 J C) 375 J D) 3116 J

[12] Find the work involved in the following processes as described on a p-V diagram for one mole of a diatomic gas.

ê. . . . . . . . . . . . . . . . . .

ê . .

Pressure (Pa) | . . (Isothermal curve)

| . .

| . . . . . . . . . . . . . . . . . .

ë_____.____________.____

1 3 Volume in m³

1. 385 J B) -385 J C) 3195 J D) -3195 J

[13] The net heat transfer between the Sun and Earth is Sun è Earth. Does the entropy of the Earth-Sun “closed” system increase (I), decrease (D) or remain the same (S) during this process? Using the sun’s radiant heat energy, life forms on Earth convert carbon dioxide, nitrogen, and water into the complicated proteins, sugars and starches of the “biomass”. Does this process increase (raise = R), decrease (lower=L), or leave unchanged (U) the entropy of the Earth + biomass? (You can write a clarifying sentence if you like.)

A) I, R B) I, L C) D, R D) D, L E) S, U

[14] You wish to increase the coefficient of performance of an ideal race car engine. The

cylinders run at 1000K. The outside air temperature is 300 K. You can do so by (i) running the cylinders at 10K hotter temperature, (ii) running the cylinders at 10K lower temperature, (iii) taking test laps on a 10K cooler day, (iv) taking test laps on a 10K warmer day. Rank the coefficient of performance of these four cases from greatest to smallest.

A) i, ii, iii, iv B) i, iii, iv, ii C) iii, iv, i, ii D) iii, i, ii, iv E) iv, i, ii, iii

[15] A box contains one mole of a gas. Consider 3 configurations: (a) each half of the box has ½ the number of particles; (b) one half of the box has all the particles; (c) one half of the box has ¾ of the particles. Which configuration has the more microstates?

A) a B) b C) c D) they are all the same E) need to know the temperature

[16] The speeds of 10 molecules are -5, -4, -3, -2, -1, 1, 2, 3, 4, 5 km/s respectively. What is the rms speed of the molecules?

A) -3 km/s B) -1 km/s C) 0 km/s D) 1 km/s E) 3 km/s