Differential equation-Temperature of an electrical component
Model the temperature of an electrical component.
Write down a differential equation that models the temperature 'T' at time t.
Let 'Τ' be the excess temperature of the component over the environment at time t. Initially the electrical component is the same temperature as its
environment, that is Τ = 0 at t = 0. The component generates heat at a rate
that corresponds to a temperature change of 'a' Kelvins per second. The
component has a cooling fan that dissipates heat at a rate that corresponds
to a temperature change that is proportional to the temperature above
ambient, with constant of proportionality 'b' per second.
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(30 pts) Newton's law of cooling says that the temperature of a body changes at a...
(30 pts) Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature). dT * = -k(T – Ta) where T = the temperature of the body (°C), t = time (min), k = the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 80 °C. Use...
2. Newton's law of cooling can be used to derive a differential equation model for the...
2. Newton's law of cooling can be used to derive a differential equation model for the temperature of an object that is placed in a cool medium. We define the variables u(t) to represent the temperature of the object at time t. We also define the parameter T to be the constant temperature of the medium. Newton's law of cooling states that the rate of change in the temperature of the object is proportional to the difference between the temperature...
Newton's law of cooling states that the rate of change in the temperature T(t) of a...
Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, * = K[M(t) - T(t)], where K is a constant. Let K = 0.05 (min) and the temperature of the medium be constant, M(t) = 295 kelvins. If the body is initially at 354 kelvins, use Euler's method with h = 0.1 min...
Newton's law of cooling states that the rate of change in the temperature T(t) of a...
Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, dT K[M(t) - T(t)], where K is a constant. Let K=0.05 (min) - 1 and the temperature of the medium be constant, dt M(t) = 294 kelvins. If the body is initially at 370 kelvins, use Euler's method with h=0.1 min to approximate...
dt Newton's law of cooling states that the rate of change in the temperature (t) of...
dt Newton's law of cooling states that the rate of change in the temperature (t) of a body is proportional to the difference between the temperature of the medium M(t) and the dT temperature of the body. That is, = K[M(1) – TCC), where is a constant. Let K = 0.03 (min) and the temperature of the medium be constant, m(t) = 295 kelvins. If the body is initially at 364 kelvins, use Euler's method with h = 0.1 min...
Question 2 You are working as a crime scene investigator and must predict the temperature of...
Question 2 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. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature), where T = the temperature of the...
All the computer work is done. Need help with hand written solution for all questions, thanks....
All the computer work is done. Need help with hand written
solution for all questions, thanks.
Freezing pipes. The Problem and Model. The project is to determine an approximation for the indoor temperature u(t) in an unheated builg. The model uses Newton's cooling law, insulation data k and a formula for the ambient outside temperature A(t) (see the background section infra) u'(t) + ku(t) = kA(t) u(0)o Assumptions and Notation. Let the daily temperature in Salt Lake City vary from...
7. (3 points) Suppose you are in a room with a temperature of 72 F. Newton's...
7. (3 points) Suppose you are in a room with a temperature of 72 F. Newton's law of cooling states that the rate at which an object cools (or heats) is proportional to the difference between the object's temperature and the ambient temperature of the room. (a) Write down a differential equation representing Newton's Law. Let T(t) be the temperature of the object that is placed in the room (b) Solve the differential equation to find T(t). (c)Suppose T(0)-80° and...
show works please 10 Points The differential equation shown below models the temperature of an 89°...
show works please
10 Points The differential equation shown below models the temperature of an 89° C cup of coffee in a 17° C room, where is it known that coffee cools at a rate of 1° C per minute. Solve the differential equation to find an expression for the temperature of the coffee at time t. 0 In the differential equation shown below y is the temperature of the coffee in C, and t is the time in minutes...
show works please 10 Points The differential equation shown below models the temperature of an 89°...
show works please
10 Points The differential equation shown below models the temperature of an 89° C cup of coffee in a 17° C room, where is it known that coffee cools at a rate of 1° C per minute. Solve the differential equation to find an expression for the temperature of the coffee at time t. 0 In the differential equation shown below y is the temperature of the coffee in C, and t is the time in minutes...
(30 pts) Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature). dT * = -k(T – Ta) where T = the temperature of the body (°C), t = time (min), k = the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 80 °C. Use...
2. Newton's law of cooling can be used to derive a differential equation model for the temperature of an object that is placed in a cool medium. We define the variables u(t) to represent the temperature of the object at time t. We also define the parameter T to be the constant temperature of the medium. Newton's law of cooling states that the rate of change in the temperature of the object is proportional to the difference between the temperature...
Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, * = K[M(t) - T(t)], where K is a constant. Let K = 0.05 (min) and the temperature of the medium be constant, M(t) = 295 kelvins. If the body is initially at 354 kelvins, use Euler's method with h = 0.1 min...
Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, dT K[M(t) - T(t)], where K is a constant. Let K=0.05 (min) - 1 and the temperature of the medium be constant, dt M(t) = 294 kelvins. If the body is initially at 370 kelvins, use Euler's method with h=0.1 min to approximate...
dt Newton's law of cooling states that the rate of change in the temperature (t) of a body is proportional to the difference between the temperature of the medium M(t) and the dT temperature of the body. That is, = K[M(1) – TCC), where is a constant. Let K = 0.03 (min) and the temperature of the medium be constant, m(t) = 295 kelvins. If the body is initially at 364 kelvins, use Euler's method with h = 0.1 min...
Question 2 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. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature), where T = the temperature of the...
All the computer work is done. Need help with hand written
solution for all questions, thanks.
Freezing pipes. The Problem and Model. The project is to determine an approximation for the indoor temperature u(t) in an unheated builg. The model uses Newton's cooling law, insulation data k and a formula for the ambient outside temperature A(t) (see the background section infra) u'(t) + ku(t) = kA(t) u(0)o Assumptions and Notation. Let the daily temperature in Salt Lake City vary from...
7. (3 points) Suppose you are in a room with a temperature of 72 F. Newton's law of cooling states that the rate at which an object cools (or heats) is proportional to the difference between the object's temperature and the ambient temperature of the room. (a) Write down a differential equation representing Newton's Law. Let T(t) be the temperature of the object that is placed in the room (b) Solve the differential equation to find T(t). (c)Suppose T(0)-80° and...
show works please
10 Points The differential equation shown below models the temperature of an 89° C cup of coffee in a 17° C room, where is it known that coffee cools at a rate of 1° C per minute. Solve the differential equation to find an expression for the temperature of the coffee at time t. 0 In the differential equation shown below y is the temperature of the coffee in C, and t is the time in minutes...
show works please
10 Points The differential equation shown below models the temperature of an 89° C cup of coffee in a 17° C room, where is it known that coffee cools at a rate of 1° C per minute. Solve the differential equation to find an expression for the temperature of the coffee at time t. 0 In the differential equation shown below y is the temperature of the coffee in C, and t is the time in minutes...
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