thermodynamics homework 4

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Using table A-6

At First State

At Final State

a) the compression work

b) the volume of the metal box at the final state is 64.28% from its initial volume, so the work will be as

Thermodynamics Copyright © by Diana Bairaktarova (Adapted from Engineering Thermodynamics - A Graphical Approach by Israel Urieli and Licensed CC BY NC-SA 3.0) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Thermodynamics

Chapter 4 homework.

Using table A-6

At First State

At Final State

a) the compression work

b) the volume of the metal box at the final state is 64.28% from its initial volume, so the work will be as

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ME 200: Thermodynamics I

Homework Submissions

Homework Problem Statements Homework 1 and 2 (Week 1) Homework 3 and 4 (Week 2) Homework 5, 6, and 7 (Week Homework 8, 9, and 10 (Week 4) Homework 11, 12, and 13 (Week 5) Homework 14, 15, and 16 (Week 6) Homework 17 and 18 (Week 7) Homework 19, 20, and 21 (Week 8) Homework 22, 23, and 24 (Week 9) Homework 25 and 26 (Week 10) Homework 27, 28, and 29 (Week 11) Homework 30, 31, and 32 (Week 12) Homework 33, 34, and 35 (Week 13) Homework 36 and 37 (Week 14) Homework 38, 39, and 40 (Week 15)

Homework Solutions Homework 1 and 2 (Week 1) Homework 3 and 4 (Week2) Homework 5, 6, and 7 (Week 3) Homework 8, 9, and 10 (Week 4) Homework 11, 12, and 13 (Week 5) Homework 14, 15, and 16 (Week 6) Homework 17 and 18 (Week 7) Homework 19, 20, and 21 (Week 8) Homework 22, 23, and 24 (Week 9) Homework 25 and 26 (Week 10)  Homework 27, 28, and 29 (Week 11) Homework 30, 31, and 32 (Week 12) Homework 33, 34, and 35 (Week 13) Homework 36 and 37 (Week 14) Homework 38, 39, and 40 (Week 15)

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Purdue University

ME 200 – Thermodynamics I – Spring 2020 ¶

Homework 4: mechanical energy and work ¶.

Part (i): "Rods from god" ¶ Part (ii): Spiderman ¶

Part (i): "Rods from god" ¶

Given: ¶.

A cylindrical rod of tungsten falls from an altitude of $1000 km$ with an initial velocity $7.4 km/s$. The rod has a diameter of $0.3 m$, length of $6 m$, and density of $19.3 g/cm^3$. Following is a calculation window to assign the given inputs:

Find: ¶

a) maximum impact kinetic energy (GJ) in the absence of drag,

b) maximum speed (km/s) of the rod neglecting air drag,

c) impact energy (GJ) for a purely vertical descent and average drag force acting on the rod of 150 kN,

d) feasibility of this concept as an alternative to explosives.

System Sketch: ¶

Assumptions: ¶

1) Acceleration due gravity is assumed to be constant and the same as on the Earth's surface.

Basic Equations: ¶

Solution: ¶, a) impact ke in the absence of drag ¶.

In the absence of drag forces, potential energy is converted to kinetic energy. If the reference frame is the Earth target, then potential energy at impact is zero and the impact kinetic energy will equal the initial potential energy plus the initial kinetic energy of the tungsten rod or

where m is the rod’s mass, g is the acceleration due to gravity, H is the rod’s altitude, and $V_0$ is the initial speed of the rod. For a cylindrical rod, the mass is determined as

The following code window implements this solution and prints the result.

b) Impact velocity in the absence of drag ¶

Based on the definition of kinetic energy

the impact velocity is

This result is implemented in the following calculation window.

This is approximately 25 times the speed of sound at sea level. However, it is only about 15% higher than the initial velocity due to the orbital speed of the satellite.

c) Impact kinetic energy with drag ¶

The rod does work against a drag force that reduces the conversion of potential to kinetic energy leading to

where $W_{drag}$ is the mechancial work againt the drag force expressed as:

This "mechanical" energy balance results from a force balance on the rod involving gravitional, drag, and inertial forces and then integrating the terms through the vertical distance resulting in mechanical energy terms. The work dissipation associated with drag would be converted to thermal energy. However, this problem is focussed on only mechanical energy terms. Calculation of the impact kinetic energy for this case is implemented in the following code cell.

The impact kinetic energy decreases by approximately 50%. However, it should be noted that the ascent would not be vertical, such that the distance travelled and drag work could be significantly greater.

d) Feasability ¶

Although the energy impact is signficant compared to explosives (equivalent to ~40 tons of TNT), there are some limitations. First of all, this approach would only be applicable to stationary targets since there is no on-board guidance system. Furthermore, the target accuracy could be subject to atmospheric conditions (e.g., wind). Another issue could be time to impact. The initial velocity would be primarily due to the orbital velocity of the satelitte, such that initial downward velocity could be low and the distance travelled to the taget could be significantly greater than the altitude. However, the approach may be particular useful for penetrating underground bunkers that contain missiles. There would be less overall damage to the surroundings than when employing explosives.

Part(ii): Spiderman ¶

Spiderman is pushing against a 540 ton (489,880 kg) train that is traveling at 30 mph (13.4 m/s). Spiderman weighs 167 lb (75.8 kg) and has a coefficient of friction between his feet and the ground of 0.8.

The distance necessary to stop the train.

Spiderman is doing mechanical work against the inertia of the train that reduces the kinetic energy to zero such that

where $m_{train}$ is the train’s mass and $V_{train}$ is the initial speed of the train. The mechanical work is the integral of the force applied through the stopping distance (d).

where F is the force applied by Spiderman to the train and d is the distance over which this force acts. The applied force is equal to the frictional force between Spiderman's feet and the ground, which depends on his weight according to

where $\mu$ is the friction coefficient between Spiderman’s feet and the ground, m_{spidey} is Spiderman’s mass, and g is the acceleration due to gravity.

Solving for d gives: $$d = \dfrac{\dfrac{1}{2}m_{train}V_{train}^2}{\mu m_{spidey}g}$$

Thermodynamics

Homework sets, helpful and interesting links.

Homework Set B

Please read the Problem Solving Guideline before beginning any problems and take the Quiz .

Please read the rules before beginning any problems.

Set 1 Reading Assignment: Chapter 1: Introductory Concepts and Definitions (ALL), Chapter 3: Evaluating Properties (ALL except 3.3.2, 3.3.5, 3.4, 3.5, 3.6, 3.7). Also, read section, "Evaluating Properties Using the Ideal Gas Model," paying special attention to example problem 3.7.

Problem 1 , Problem 2 , Problem 3 , Problem 4 , Problem 5 , Problem 6 , Problem 7 , Survey Set 1

Set 2 Reading Assignment: Chapter 3: Evaluating Properties (ALL except 3.3.2, 3.3.5, 3.4, 3.5, 3.6, 3.7). Also, read section, "Evaluating Properties Using the Ideal Gas Model," paying special attention to example problem 3.7.

Problem 1 , Problem 2 , Problem 3 , Problem 4 , Problem 5 , Problem 6 , Problem 7 , Problem 8 , Survey Set 2

Set 3 Reading Assignment: Chapter 3: Evaluating Properties, sections 3.3.2, 3.3.5, 3.4, 3.5, 3.6, 3.7. Chapter 2: Energy and the First Law of Thermodynamics (ALL except 2.6). Chapter 4: Control Volume Analysis Using Energy (ALL except 4.4. Note: 4.3.3 is most inportant and has several excellent examples).

Problem 1 , Problem 2 , Problem 3 , Problem 4 , Problem 5 , Problem 6 , Problem 7 , Survey Set 3

Set 4 Reading Assignment: Chapter 4: Control Volume Analysis Using Energy, section 4.4: Transient and Closed Systems

Problem 1 , Problem 2 , Problem 3 , Problem 4 , Problem 5 , Problem 6 , Problem 7 , Problem 8, Survey Set 4

Set 5 Reading Assignment: Chapter 3: Evaluating Properties, sections 3.3.2, 3.3.5, 3.5, 3.6, 3.7, on Cp and latent heats.

Problem 1 , Problem 2 , Problem 3 , Survey Set 5

Set 6 Reading Assignment: Chapter 5: The Second Law of Thermodynamics, sections 5.1, 5.2. Chapter 6: Using Entropy (ALL).

Problem 1 , Problem 2 , Problem 3 , Problem 4 , Problem 5 , Problem 6 , Problem 7 , Problem 8 , Problem 9, Survey Set 6

Set 7 Reading Assignment: Chapter 2: Energy and the First Law of Thermodynamics, section 2.6. Chapter 5: The Second Law of Thermodynamics, sections 5.3, 5.5, 5.6. Chapter 8: Vapor Power Systems (ALL). Chapter 10: Refrigeration and Heat Pump Systems (ALL except 10.7).

Problem 1 , Problem 2 , Problem 3 , Problem 4 , Problem 5 , Problem 6 , Problem 7 , Problem 8, Survey Set 7