# Formula for relating time and heat gained for closed system

• Allen Dowe
In summary, the temperature inside the system increased more slowly than the temperature outside the system.
Allen Dowe
This is for work. I need to make a table for a client.
What we did: had two different closed systems, only difference is material. We had frozen goods in both containers, the containers were both removed from the cooled surroundings they were in and placed outside. The temperatures were taken for both containers every minute.
What I need is a formula or something to help me create a table that will show a relationship between the outside temperature and the time it takes the temperature inside the system to get to a certain temperature (not yet chosen). I will be making 2 Tables one for each container.
NOTE: exclude variables like wind, humidity, pressure, being that this table is meant for consumers to see. they do not need exacts.

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The data you collected has the information you need. Have you plotted the data in excel or sim.? Add a trendline, the formula for that trendline should follow Newtons law of cooling:
http://formulas.tutorvista.com/physics/Newton-s-law-of-cooling-formula.html
http://en.wikipedia.org/wiki/Convective_heat_transferIgnoring wind may be a poor assumption, forced convection heat transfer can be orders of magnitude greater than natural convection heat transfer (that's why we blow on hot food and cars have radiator fans etc)

russ_watters
Thank you sir, I appreciate it! And yes i agree, but it would leave me with too much variability to make a chart I think. What do you say?

Explain 'too much variability'.
If your data is poor then anything you glean from it will also be poor.

The goal is for consumers to see the comparison of our product to their current product. Since the conditions were exact for the two systems (held at same time/place) i feel it should be alright to assume fair conditions.

By too much variability I mean is there would be sooo much extra data that would almost be considered irrelevant from a consumer perspective. Your thoughts?

I don't understand what you're saying.
It's up to you to decide what data to give the consumer. Give them as much as you see fit.
I think simply graphing what you have will be fine. The consumer will see your new product warms up slower than the current.
Like this:

(obviously, your products are increasing temp rather than cooling)

## What is the formula for relating time and heat gained for a closed system?

The formula is Q = mcΔT, where Q is the heat gained, m is the mass of the system, c is the specific heat capacity of the material, and ΔT is the change in temperature.

## Why is this formula important in scientific research?

This formula allows scientists to accurately calculate the amount of heat gained or lost in a closed system over a period of time. This is important in many fields of research, such as thermodynamics, chemistry, and engineering.

## How is time related to heat gained in a closed system?

Time is directly proportional to the amount of heat gained in a closed system. This means that as the time increases, so does the heat gained. Similarly, if the time decreases, the heat gained also decreases.

## What are the units of measurement for the variables in this formula?

The units for Q are joules (J), for m are kilograms (kg), for c are joules per kilogram per degree Celsius (J/kg°C), and for ΔT are degrees Celsius (°C).

## Can this formula be applied to open systems?

No, this formula is specifically for closed systems where there is no exchange of matter with the surroundings. It cannot be applied to open systems as they involve the transfer of matter and energy.

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