Hello PF. I am an undergraduate in physics doing some work in a research lab at school and I need some help with a time-constant calorimetry experiment I am working on.(adsbygoogle = window.adsbygoogle || []).push({});

I am attempting to compute the temperature as a function of time of a small sample of copper that I am heating. I am modeling the setup as if the sample, the heater, and the thermometer are all in perfect thermal equilibrium (infinite thermal conductance between all three) and some thermal resistance R to a constant temperature reservoir to which heat is lost.

I have come up with the following differential equation to describe this situation:

d/dt(Q) = C*d/dt(T) + R(T-Ts) where Q is the heat added, T is the temp of the sample/thermometer, R is the thermal resistance between the sample and the reservoir and Ts is the temp of the reservoir.

I am hoping that someone can help me determine if the above is correct and if so give me some pointers on how to solve this diff-eq. I believe this is a linear coupled system and I don't know where to start. I really appreciate the help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Thermo diff-eq problems

**Physics Forums | Science Articles, Homework Help, Discussion**