# Homework Help: Electric analogies to thermal systems

1. Dec 4, 2008

### Nissen, Søren Rune

This is translated, and it's problem j of j problems, so I might have missed writing down something important along the way. If I have, please feel free to request additional data.

Inside a box of polyurethane foam, a 60 W lightbulb is turned on.

Before the lightbulb is turned on, the temperature, inside and outside of the box, is 20 degrees celcius.

The temperature inside the box can be modelled like this:

T(t) = 346K + (293K - 346K)*e^(-t/90).

Inside the box is a temperature sensor. When lowered into a thermal reservoir at 90 degrees celcius and kept in there for a short while, the sensor reports the temperature like this:

T(t) = 362K + (300K - 362K)*e^(-t/15s)

The sensor is a platinum wire resistor, whose resistance changes linearly with the temperature (at least, inside the area I'm currently working in).

Problem Statement

Create a single thermal analogy that includes both the polyurethane box and the PT100 sensor. The measured temperature curve must be graphed for the single system, and the effect the sensors time constant has on the measurement of the temperature must be discussed.

The attempt at a solution

Showing the lightbulb as a current source, the polyurethane box as a resistor, the capacitor on the right hand side of this is the air - to make the electric analogy, the voltage across the capacitor is equivalent to the temperature differential between the air inside and outside of the box.

http://img183.imageshack.us/img183/4328/withpt100mh9.jpg [Broken]

Now, on the right hand side, I've made what I believe is a thermal analogy to the temperature sensor, but this is the part where I'm not certain - if this isn't the right way, I could really use a hint.

Last edited by a moderator: May 3, 2017