PHYS 212 – Spring 2014 MOCK MIDTERM EXAM #1

This exam is about half as long as the actual exam. Give yourself 55 minutes to complete it (the actual midterm is 110 minutes in duration).

For your information, I have indicated for each question whether it is algebraic, numerical, or qualitative. This information is not included on the actual midterm.

Assume that all answers contain an appropriate number of significant figures.

A list of data and conversion factors is provided on page 5.

1 (alg)

If we double the temperature of an ideal gas, by what factor has the average velocity of the gas molecules changed? A) ½ B) 2 C) ¼ D) 4

E) √2

2 (num)

A 50 cm3 gas cylinder contains 0.10 moles of argon gas at a temperature of 20°C. The gas then undergoes isochoric heating to a final temperature of 300°C. What is the final pressure of the argon? The molar mass of argon is 39.95 g/mol A) 101.3 kPa B) 4190 kPa C) 4900 kPa D) 9500 kPa E) 9920 kPa

3 (qual)

Is it possible to transfer heat from a cold reservoir to a hot reservoir?

A) No, because this is forbidden by the first law of thermodynamics. B) No, because this is forbidden by the second law of thermodynamics. C) Yes, but as of 2013 it has not been accomplished. D) Yes, it happens naturally all the time. E) Yes, but it requires external work to be done.

PHYS 212 Spring 2014 MOCK Midterm Exam #1 Page 2 of 5

4 (num)

A Carnot engine operates between reservoir temperatures of 300 K and 700 K, drawing 60 kJ of heat from the 700 K reservoir in each cycle. How much heat is dumped into the 300 K reservoir in each cycle? A) 26 kJ B) 34 kJ C) 36 kJ D) 38 kJ E) 42 kJ

5 (num)

The figure shows a 𝑝𝑉 diagram for 0.95 mol of gas that undergoes the process 1 → 2. The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1. What is the final temperature of the gas?

A) -158 °C B) -13 °C C) 29 °C D) 59 °C E) 115 °C

6 (qual)

Consider equal masses of water and iron that are initially in thermal equilibrium. The same amount of heat is added to each one. Which of the following statements is true? A) They remain in thermal equilibrium. B) They are no longer in thermal equilibrium; the iron is warmer. C) They are no longer in thermal equilibrium; the water is warmer. D) It is impossible to say without knowing the exact mass involved. E) It is impossible to say without knowing the exact amount of heat involved.

PHYS 212 Spring 2014 MOCK Midterm Exam #1 Page 3 of 5

7 (alg)

𝑛 moles of an ideal gas with specific heat ratio 𝛾 has an initial temperature, volume, and pressure of 𝑇1, 𝑉1, and 𝑝1, respectively. The gas is then expanded adiabatically, resulting in a final volume and pressure of 𝑉2 and 𝑝2, respectively. 𝑅 is the universal gas constant. What is the final temperature, 𝑻𝟐?

A) 𝑇2 =𝑝1𝑉1

𝑛𝑅

B) 𝑇2 = 𝑇1 (𝑉2

1)

𝛾

C) 𝑇2 = 𝑛𝑅𝑝1

D) 𝑇2 =1

𝑛𝑅ln

𝑉1

𝑉2

E) 𝑇2 = 𝑇1 (𝑉1

𝑉2)

𝛾−1

8 (num)

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe then narrows to 2.50 cm. Consider water to be an ideal fluid. What is the pressure in the narrower region? A) 4.00 kPa B) 4.61 kPa C) 5.82 kPa D) 6.42 kPa E) 7.50 kPa

PHYS 212 Spring 2014 MOCK Midterm Exam #1 Page 4 of 5

9 A heat engine using a diatomic gas follows the cycle shown in the figure. a) Determine the pressure, volume, and

temperature at point 1. b) For each process in the cycle, find 𝑾𝒔, 𝑸,

and 𝚫𝑬𝐭𝐡. Display your results in the table below.

c) How much work does this engine do per cycle?

d) What is the thermal efficiency of this heat engine?

Process 𝑾𝒔 (J) 𝑸 (J) 𝚫𝑬𝐭𝐡 (J)

1 2

2 3

3 1

PHYS 212 Spring 2014 MOCK Midterm Exam #1 Page 5 of 5

Avogadro’s Number 𝑁𝐴 = 6.023 × 1023mol−1 Universal Gas Constant 𝑅 = 8.31 J/mol∙K Boltzmann’s Constant 𝑘𝐵 = 1.38 × 10−23 J/K Conversion 1 liter = 10-3 m3 1 u = 1.661 x 10-27 kg 1 atm = 101.3 kPa SI base units: meter, kilogram, second, Kelvin, mole, Ampere, candela (the last two of

these haven’t been covered yet)