prep-for-midterm-1-phy-1321

Studocu is not sponsored or endorsed by any college or university Prep for Midterm 1 PHY 1321 Principles of Physics I (University of Ottawa) Studocu is not sponsored or endorsed by any college or university Prep for Midterm 1 PHY 1321 Principles of Physics I (University of Ottawa) Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

PHY 1321/1331 - Midterm Prep 2019 Your best bud First year course University of Ottawa Ottawa, ON, Canada Fall 2019 c circlecopyrt Your best bud, Ottawa, Canada, 2019 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

Contents MIDTERM PREPARATION 2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part 1 - Second Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Part 1 - Version 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Part 2 - Version 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

MIDTERM PREPARATION 2019 Part 1 1. A reversible heat engine has a PV diagram shown in the graph. The net heat transferred between the engine and environment in one cycle is approximately? (A) -0.5 kJ (B) +0.5 kJ (C) -0.6 kJ (D) +0.6 kJ (E) none of the above (A) -0.5 kJ (B) +0.5 kJ (C) -4.2 kJ (D) +4.2 kJ (E) none of the above (A) -0.7 kJ (B) +0.7 kJ (C) -0.6 kJ (D) +0.6 kJ (E) none of the above 2. Given is the two-dimensional gas made out of diatomic molecules. At sufficiently high temperatures the gas molecules are free to move around within the two-dimensional place, as well as to rotate and oscillate. What is the the average energy E avg and the C p of a single molecule of the gas, at [low or intermediate or high]] temperatures [ T < 150 K or 250 K < T < 600 K or T > 3000 K ]? (A) E avg = 1 2 mv 2 x + 1 2 mv 2 y and C p = R (B) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 Iω 2 and C p = 3 2 R (C) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 I 1 ω 2 1 + 1 2 I 2 ω 2 2 + 1 2 mv 2 osc + 1 2 kr 2 and C p = 4 R (D) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 Iω 2 + 1 2 I 2 ω 2 2 + 1 2 mv 2 osc + 1 2 kr 2 and C p = 5 2 R (E) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 Iω 2 + 1 2 mv 2 osc + 1 2 kr 2 and C p = 7 2 R 3. The figure shows the distribution of the molecular speeds of a gas for two different temperatures T 1 (solid) and T 2 (dashed). Which of the following statement is true: BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

cold reservoir? (A) 100 (B) 150 (C) 200 (D) 250 (E) none of the above (A) 100 (B) 150 (C) 200 (D) 250 (E) none of the above (A) 100 (B) 150 (C) 200 (D) 250 (E) none of the above 7. (Four or Five or Three) moles of an ideal monoatomic gas are initially in the 100L container at pressure [500kPa or 400kPa or 400kPa]. The gas is released to fill an additional volume of a vacuum system (initially at P = 0) of volume 400L, in such way that no heat is exchanged with the surroundings, and no gas is lost. What is the final temperature of the gas? (A) 237K (B) 329K (C) 514K (D) 549K (E) none of the above (A) 237K (B) 329K (C) 514K (D) 549K (E) none of the above (A) 237K (B) 329K (C) 514K (D) 549K (E) none of the above Part 1 - Second Version 1. Couvier’s Beaked Whale can dive to depths of [3 or 2 or 1.1] kilometer. What is the total pressure they experience at this depth? ( ρ = 1020 kg/m3 and 10 5 N/ m 2 = 1 ATM, g = 9.81 m/ s 2 .) (A) 9 ATM (B) 101 ATM (C) 198 ATM (D) 301 ATM (E) none of the above (A) 9 ATM (B) 101 ATM (C) 201 ATM (D) 301 ATM (E) none of the above (A) 9 ATM (B) 111 ATM (C) 198 ATM (D) 301 ATM (E) none of the above 2. A reversible heat engine has a pV diagram shown on the graph. The net heat transferred between the engine and environment in one cycle is approximately: (A) 0 kJ (B) 2.0 kJ (C) 4.2 kJ (D) 6.9 kJ (E) 7.5 kJ (A) 0 kJ (B) 2.0 kJ (C) 4.2 kJ (D) 5.5 kJ (E) 7.5 kJ (A) 0 kJ (B) 5.6 kJ (C) 6.9 kJ (D) 7.5 kJ (E) 8.2 kJ Page 3 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

3. A heat pump has a coefficient of performance [3.0 or 4.0 or 5.0]. How much heat is exhausted to the hot reservoir when [300 kJ or 400 kJ or 400 kJ] of heat are removed from the cold reservoir? (A) 500 kJ (B) 480 kJ (C) 450 kJ (D) 400 kJ (E) none of the above (A) 530 kJ (B) 480 kJ (C) 450 kJ (D) 400 kJ (E) none of the above (A) 530 kJ (B) 500 kJ (C) 450 kJ (D) 400 kJ (E) none of the above 4. Given is the two-dimensional gas made out of diatomic molecules. At sufficiently high temperatures the gas molecules are free to move around within the two-dimensional place, as well as to rotate and oscillate. What is the the average energy E avg and the C v of a single molecule of the gas, at [low or intermediate or high]] temperatures [ T < 150 K or 250 K < T < 600 K or T > 3000 K ]? (A) E avg = 1 2 mv 2 x + 1 2 mv 2 y and C v = R (B) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 Iω 2 and C v = 3 2 R (C) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 I 1 ω 2 1 + 1 2 I 2 ω 2 2 + 1 2 mv 2 osc + 1 2 kr 2 and C v = 4 R (D) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 Iω 2 + 1 2 I 2 ω 2 2 + 1 2 mv 2 osc + 1 2 kr 2 and C v = 5 2 R (E) E avg = 1 2 mv 2 x + 1 2 mv 2 y + 1 2 Iω 2 + 1 2 mv 2 osc + 1 2 kr 2 and C v = 7 2 R 5. In an [isothermal or isobaric or isovolumetric] process: (A) the internal energy is constant (B) work is transferred between a system and its surroundings (C) no heat is transferred between a system and its surroundings. (D) work and heat are both transferred between the system and its surroundings. (E) of the above is correct statement about the isothermal process - (A) the internal energy is constant (B) the volume remains constant (C) The heat is transferred between a system and its surroundings (D) work and heat are both transferred between the system and its surroundings. (E) of the above is correct statement about the isobaric process - (A) the internal energy is constant (B) there is no work transferred between the system and its surroundings. (C) no heat is transferred between a system and its surroundings Page 4 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

Given: ρ Cu = 8 . 94 g cm 3 ; α Cu = 17 × 10 − 6 K − 1 ; c Cu = 385 J kg ◦ C , A cylinder = 2 πRh + 2 πR 2 ; c water = 4186 J kg ◦ C ; c ice = 2090 J kg ◦ C ; c steam = 2010 J kg ◦ C ; L melting = 3 . 3 × 10 5 J kg ; L vaporization = 2 . 26 × 10 6 J kg ; P = eσAT 4 ; σ = 5 . 67 W K 4 m 2 3. (a) At 50.0 m below the surface of the sea (density = 1025 kg m 3 ), where the temperature is 4.00 ◦ C, a diver exhales an air bubble having a volume o 1.00 cm 3 . If the surface temperature of the sea is 23.0 ◦ C, what is the volume of the bubble just before it breaks the surface? (b) A rigid tank having a volume of 0.100 m 3 contains helium gas at 150 atm. How many balloons can be inflated by opening the valve at the top of the tank? Each filled balloon is a sphere 0.200 m in diameter at an absolute pressure of 1.20 atm. (c) A [3.00 mol or 1.00 mol] sample of an ideal monoatomic gas is takes through the cycle shown. The process A −→ B is a reversible isothermal expansion. Calculate (i) the net work done by the gas, (ii) the energy added to the gas by hear, (iii) the energy exhausted from the gas by heat, and (iv) the efficiency of he cycle. 4. A sample of diatomic gas with specific heat ratio γ = 5/3, confined to a cylinder of initial volume of 20 liters, is carried through a closed cycle. The gas is initially at 1.00 atm and at 243K. First, its pressure is doubled under constant volume. Then, it expands adiabatically to three times the original volume. Then the gas is cooled down at constant volume to of 0.16 of the original pressure. Finally, the gas is compressed adiabatically i to its original volume.and pressure. (a) Draw a PV diagram of this cycle. (b) Determine the pressure of the gas at the end of the adiabatic expansion. (c) Find the temperature of the gas at the end of the adiabatic expansion. (d) Find the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle? (f) Find the heat transferred to gas from hot reservoir in one cycle (g) What would be the efficiency of an engine based on this cycle? Page 6 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

5. In 1816 Robert Stirling, a Scottish clergyman, patented the Stirling engine, which has found a wide variety of applications ever since. Fuel is burned externally to warm one of the engine’s two cylinders. A fixed quantity of the inert gas moves cyclically between the cylinders, expanding in the hot one and contracting in the cold one. Figure below represents a model for its thermodynamic cycle. Consider n mol of an ideal monoatomic gas being takes once through the cycle, consisting of two isothermal processes at temperatures 3 T i and T i and two constant-volume processes. Determine, in terms of n , T and T i : (a) the net energy transferred by heat to the gas. (b) its efficiency. 6. Given one mole of N 2 gas at [37 ◦ C or 27 ◦ C] (molar mass of N 2 is 28 g), (a) Use Maxwell Boltzmann distribution to write the case-specific full expression for the number of N 2 molecules having speeds between [730 m/s and 732 m/s or 320.5 m/s to 321.5 m/s] . (The expression has to contain data specific for this problem - but there is no need to finish the calculations!) (b) Find the most probable velocity of N 2 at the temperature given. (c) At what temperature would the rms velocity of N 2 gas molecules be the same as in part (b)? (d) Demonstrate that the most probable velocity of gas molecules is indeed equal to V MP = ( 2 kT m ) 1 2 (e) (EXTRA) What is the expected value of γ (gamma) for N 2 gas in this temperature? (f) (EXTRA) Consider a a simple heat engine operating in a cycle corresponding to a rectangle on the pV diagram. How does its efficiency depend on the type of gas being used (its Cv). Show your calculations 7. (a) Present detailed proof of one of the two below: (i) using the summary of thermodynamic processes table (from your formula sheet) and known Laws of Thermodynamics, prove that C p = C v + R . (ii) using the summary of thermodynamic processes table (from your formula sheet) and known Laws of Thermodynamics, prove that C p C v = γ . Page 7 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

5. Ratio of the [ N V rms or N V mp or N V avg ] number of molecules that have speed equal to [ V rms or V mp or V avg ], to [ N V mp or N V rms or N V mp ] the number of molecules having speed of [ V mp or V rms or V mp ] is given by: (A) 5 3 e − 1 2 (B) 2 3 e 1 2 (C) 3 2 e − 1 2 (D) 2 3 e − 1 2 (E) none of the above (A) 5 3 e − 1 2 (B) 2 3 e 1 2 (C) 3 2 e − 1 2 (D) 2 3 e − 1 2 (E) none of the above (A) 5 3 e − π − 1 2 (B) 4 π e 4 − π π (C) 3 2 e − 1 2 (D) 2 3 e − 1 2 (E) none of the above 6. In an adiabatic process [20 J or 25 J or 30 J] of work are done on each mole of a gas. If the gas has 5 degrees of freedom, how much does its temperature change? Answer in terms of R. (A) 20/R (K) (B) 10/R (K) (C) 20/7R (K) (D) 8/R (K) (E) none of the above (A) 20/R (K) (B) 10/R (K) (C) 20/7R (K) (D) 8/R (K) (E) none of the above (A) 20/R (K) (B) 10/R (K) (C) 20/7R (K) (D) 8/R (K) (E) none of the above Part 2 - Version 2 1. A U-tube of uniform cross-sectional area, open to the atmosphere, is partially filled with mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as shown. For h 2 = 1.00 cm, determine the value of h 1 . 2. A 1.00 kg iron cube is taken from a forge at 900 ◦ C and dropped into 4.00 kg of water at 10.0 ◦ C. Assuming that no energy is lost by heat to the surroundings, determine (a) final temperature of the system. (b) the change of the volume of the iron cube as result of its temperature change (c) the power radiated by the iron cube just before it was dropped into the water, and after the final temperature was established. 3. A 5.00 L sample of a diatomic ideal gas with specific heat ratio 9/7, confined to a cylinder, is carried through a closed cycle. The gas is initially at 2.00 atm and at 600 K. First, its pressure is tripled under Page 9 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652

constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Determine the volume of the gas at the end of the adiabatic expansion. (c) Find the temperature of the gas at the start of the adiabatic expansion. (d) Find the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle? (f) Determine C v and C p for this gas 4. A Carnot heat engine uses a steam boiler at 100 ◦ C as the high-temperature reservoir. The low- temperature reservoir is the outside environment at 20.0 ◦ C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W. (a) Determine the useful power output of the heat engine. (b) How much steam will it cause to condense in the high-temperature reservoir in 1.00 h? Page 10 BEST BUD APPROVED Downloaded by Kayla Dutson (dutson.kayla@gmail.com) lOMoARcPSD|31431652