EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1, Problem 19P
You are working as a crime-scene investigator and must predict the temperature of a homicide victim over a 5-hr period. You know that the room where the victim was found was at 10°C when the body was discovered.
(a) Use Newton's law of cooling (Prob. 1.14) and Euler's method to compute the victim's body temperature for the 5-hr period using values of
(b) Further investigation reveals that the room temperature had actually dropped linearly from 20 to
(c) Compare the results from(a) and (b) by plotting them on the same graph.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The time evolution of the temperature of an object follows the Newton's cooling laws
dT
dx
=
-k(T - Ts),
where the term k = 2.2 (1/s) is the heat transfer constant, and Tg = 25.6° C is the ambient temperature.
The initial temperature of the object at time t = = 0 is T(t = 0) = 200°C.
°C
Use the Euler's method, and a time step of h=0.2s, calculate:
When t = = 0.2s, T =
°C
When t 1s, T =
A solid steel cube is stored in a freezer, where the temperature is −20.0 ̊C. While the cube is in the freezer, you measure its side length (L) to be 1.75050 meters. The cube is then placed outside for a long time, so that the temperature of the cube reaches the temperature of the air outside. As a result, the side length increases to 1.75170 meters due to thermal expansion. The coefficient of linear expansion for steel is 12.0×10−6 ̊C−1.
(a) What is the temperature of the air outside? Give your answer in degrees Celsius ( ̊C).
(b) What is the volume of the cube when its temperature is 20.0 ̊C? Give your answer in cubic meters (m3).
While performing the experiment of Stefan's- Boltzmann Constant, Mass of disc and Area of
the disc observes are 7 gram and 56.52 cm2, respectively. If the temperature of the metallic
hemisphere is 50 °C and steady state temperatures of copper is 46.60 °C. Determine the value
of Stefan's - Boltzmann Constant.
Given: Slope of the graph, dT/dt =0.05 °K/sec and specific heat of copper, C = 0.385 KJ/g °K.
Select one:
O a.
W
5.28 x 10-8
m2K4
Ob.
W
4.28 x 10-8.
m²K4
O c.
W
5.28 x 10-11.
m2K4
O d.
W
4.28 x 10-11
m²K4
Chapter 1 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 1 - Use calculus to solve Eq. (1.9) for the case where...Ch. 1 - 1.2 Repeat Example 1.2. Compute the velocity to ...Ch. 1 - Rather than the linear relationship of Eq. (1.7),...Ch. 1 - For the free-falling parachutist with linear drag,...Ch. 1 - Compute the velocity of a free-falling parachutist...Ch. 1 - 1.6 The following information is available for a...Ch. 1 - The amount of a uniformly distributed radioactive...Ch. 1 - A group of 35 students attend a class in a room...Ch. 1 - A storage tank contains a liquid at depth y, where...Ch. 1 - For the same storage tank described in Prob. 1.9,...
Ch. 1 - 1.11 Apply the conservation of volume (see Prob....Ch. 1 - In our example of the free-falling parachutist,...Ch. 1 - 1.13 Suppose that a spherical droplet of liquid...Ch. 1 - Newtons law of cooling says that the temperature...Ch. 1 - As depicted in Fig. P1.15, an RLC circuit consists...Ch. 1 - 1.16 Cancer cells grow exponentially with a...Ch. 1 - 1.17 A fluid is pumped into the network shown in...Ch. 1 - The velocity is equal to the rate of change of...Ch. 1 - You are working as a crime-scene investigator and...Ch. 1 - 1.21 As noted in Prob. 1.3, drag is more...Ch. 1 - 1.22 As depicted in Fig. P1.22, a spherical...Ch. 1 - As described in Prob. 1.22, in addition to the...Ch. 1 - As depicted in Fig. P1.24, the downward deflection...Ch. 1 - 1.25 Use Archimedes’ principle to develop a...Ch. 1 - Beyond fluids, Archimedes principle has proven...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
|4.2| = ?
Basic Technical Mathematics
Analytic Functions. Find fz=ux,y+ivx,y with u or v as given. Check by the Cauchy Reimann equations for analyti...
Advanced Engineering Mathematics
(a) Show that (x) = x2 is an explicit solution to xdydx = 2y on the interval (, ). (b) Show that (x) = ex x is...
Fundamentals of Differential Equations (9th Edition)
Skill Practice a. Write the set represented by the graph in interval notation and set-builder notation. b. Give...
College Algebra (Collegiate Math)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- When an object is removed from a furnace and placed in an environment with a constant temperature of 80°F, its core temperature is 1500°F. One hour after it is removed, the core temperature is 1150°F. (a) Write an equation for the core temperature y of the object t hours after it is removed from the furnace. (Round your coefficients to four decimal places.) y(t) = (b) Find the core temperature 8 hours after the object removed from furnace. (Round your answer to one decimal place.) OFarrow_forwardJes 1:01 i docs.google.com/forms what is the Physicists recognize four fundamental forces.* Flectrical force O - Gravitational force -Strong nuclear force Weak nuclear force O -Muscular force Force of friction Ff is described by • Ff = µN * O p synovlal fluld in the Joints P -coefficient of fraction between two surface in The temperature of the human body is normally about 98.6°F.calculate the temperature of the body "C* oC = (5/9)x(oF-32) =5/9(98.6- 32)-37 oc oc=(9/5)x(of -32) =9/5(98,6-32) =13,3 Under resting conditions the body energy is being used as follows * O 27% by the liver and splee O 20-%by the skeletal musules Under resting conditions the body energy is being used as follows. O 19% by the brain. 15% by the kidney. We can write the first law of thermodynamics as: * O AU-AQ -A.. O AU-AQ +AW. 1kcal = J O 1 Kcal =4184j. O O O Oarrow_forwardConsider an experimental structure required to always have constant pressure. For this purpose, a collapsible compartment has been installed that expands and contracts to adjust the volume of air inside the structure for maintaining constant air pressure of 1 atm. Given the total volume of air inside the structure was 100,000 m' when the compartment was fully collapsed, solve the following: If a constant pressure is to be maintained while the temperature varies from 0°F to 150°F, find the volume of air that the compartment holds when it expands to the maximum. For the temperature transition mentioned above, find the change in internal energy undergone by the air in the structure. Also, find the work done by the compartment while it expands. Assume air to be an ideal gas.arrow_forward
- Physical Applications of First-Order DE According to Newton’s law of cooling, the rate at which the temperature of a body changes is proportional to the difference between the instantaneous temperature of the body and the temperature of the surrounding medium. A body cools in air of constant temperature 20 0C according to this law. Ten minutes after the body began to cool, its temperature was observed to be 75 0C, and 10 minutes later its temperature was 50 0 What was its temperature when it began to cool?arrow_forwardObtain the mathematical model of the thermal system in Fig. 1. Note: Consider the heat transmitted by convection q1(t) and q2(t), and the heat given by a resistance q(t). dT1(t) (a) Variation of heat inside d(t) dT2(t) (b) Variation of heat in the wall d(t) Та T2 T1 min q1 A1 A2 Fig.1 Consider p1, p1, and Cp1, Cp2 constants. U1 and U2 are overall heat transfer coefficients, which are constants. As is the surface area for heat losses to ambient. T1> Ta and T2> Ta (inlet temperatures are higher than ambient temperature).arrow_forward3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x, t) if the bar is made of cast iron. Material a (cm²/s) Silver 1.71 Copper 1.14 Aluminum 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materialsarrow_forward
- Give True or False for the following: 1.In liquids and gases, heat transmission is caused by conduction and convection 2.The surface geometry is the important factor in convection heat transfer 3. The heat transfer by conduction from heated surface to the adjacent layer of fluid, 4. The heat transfer is increased in the fin when &> 1 5.The unit of the thermal diffusivity is m²/s 6. Temperature change between the materials interfaces is attributed to the thermal contact resistance 7. A material that has a low heat capacity will have a large thermal diffusivity. 8. Heat conduction flowing from one side to other depends directly on thickness 9.Fin efficiency is the ratio of the fin heat dissipation with that of no fin 10.The critical radius is represented the ratio of the convicted heat transfer to the thermal conductivityarrow_forwardSolve this Differential Equation question applying the Newton’s law of cooling and heating: 1.) It was noon on a cold December day in Tampa: 16°C. Detective Tavlor arrived at the crime scene to find the sergeant leaning over the body. The sergeant said there were several suspects. If they knew the exact time of death, then they could narrow the list. Detective Taylor took out a thermometer and measured the temperature of the body: 34.5°C. He then left for lunch. Upon returning at 1:00 P.M., he found the body temperature to be 33.7°C. When did the murder occur? |Hint: Normal body temperature is 37°C.|arrow_forwardA J- type thermocouple is used to measure the temperature in a heating process. Sheath material used is SS316. The length of the sheath is 13mm and thickness is 0.3mm. Find the time constant of the sheath. Material Q(kg/m3)s(J/Kg - °c)K(W/m-k) Platinum 21450 130 71.6 SS304 8030 500 21.4 SS316 7990 500 21.4 SS410 7750 460 24.9 Air 1.20 1005 0.025 MgO Powder 3580 877 26.8 Silicon compound3210 800 3 Time constant of the bare material is, T=arrow_forward
- We performed the experiment to measure the thermal conductivity of 2 materials (Brass & Steel) in the laboratory and measured the following tabulated values: Material 1 - BRASS (Diameter = 25mm) Power Temperature (°C) Q' (W) 2 3 4 6 7 8 1 5 9 14.6 78.9 77.5 76 50.2 46.7 42.4 36.1 34.6 33.6 Material 2 - STEEL (Diameter = 25mm) Power Temperature (°C) 7 Q' (W) 14.25 2 3 1 9 88.6 87.4 85 34.1 33.4 32.7 CALCULATE THE FOLLOWING: MATERIAL 1 - BRASS Calculation for Brass Quantities Calculated Values Power (Q') W Area of cross section (A) m2 Difference in Temperature between two points (AT) °C Difference in distance between two points (Ax) m Thermal conductivity of brass (k,) W/m'C MATERIAL 2 - STEEL Calculation for Steel Quantities Calculated Values Power (Q') W Area of cross section (A) m? Difference in Temperature between two points (AT) "C Difference in distance between two points (Ax) m Thermal conductivity of steel (k,) W/m°Carrow_forwardBased on your equations for the above problem, solve for the extension of the spring (in meters) when the variables have values as follows: angle A is 74.79 degrees angle B is 44.36 degrees spring constant k is 123.77 N/m mass m2 is 2.52 kgarrow_forwardHeat Transfer question In order to cool down a hot steel sphere (its diameter is 5 cm), CO2 gas is blown over it through a pipe with a diameter of 10 cm. The CO2 gas is kept at atmospheric pressure while moving through a smooth pipe at a speed of 6 m/sec. The gas temperature entering the pipe is 300K and exiting the pipe is 340 K. The pipe temperature at the entrance is 350K and at the exit is 550K. The sphere is located just about the pipe exit. Find the convective heat transfer coefficient of the gas moving in the pipe, the heat transfer rate at the pipe and the pipe length. What is the surface temperature of the sphere if the heat transfer rate between the sphere and the gas is 7W and its surface temperature is higher than the gas?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY