
Room Temperature Gain
I know this is a basic question, but I can't seem to find the correct equation anywhere....
I have a piece of equipment (running continuously) that is contributing 70,000 BTU to the space. Assume the volume of the space to be 33,000 cubic feet.
I am looking for the correct equation to determine the increase in ambient temperature in the space.
Would I use: BTU/(1.08*Volume of Room) = Temp Rise

The solution is not as simple as you'd think.
The way you have phrased the question, you have a room sitting there at X degrees.
Then you add 70,000 btu/h (I assume you mean btu/h, rather then btu, since you mention it's running continuously).
So you say you are constantly adding heat. This means the temp will continue to rise. You make no mention of a way to dissipate the heat or remove the heat (ie cool...) from the room. Essentially, the answer to the question as you've phrased it is that after a very long time, the room will become the same temperature as the hottest surface of the equipment you placed in the room.
This is probably not what you mean.
You either want to know how much the room temp will rise due to a certain discrete addition of heat (ie you have a room, and then you add 70,000 btu (note, not btu/h) to it). This is fairly straight forward, as you could calculate the heat capacity of the air (based on a constant multiplied by the mass of the air in the room). Then it'd be heat added * heat capacity = temperature rise.
What you probably mean is how hot will the room become if you have some source of cooling in the room (where you know the CFM and the discharge temp), and then you add this piece of equipment.
You reference the good ole sensible heat equation. I guess we can assume you are only adding sensible heat (boy it's a lot easier that way...).
Heat = 1.085 * delta T * cfm
You need to start by considering the room before you add the equipment. You will need to know the current temp of the room, the cooling discharge air temp, and the cfm. You can then calculate the current heat load of the room.
Your new heat load = current heat load + 70,000 btu/h (again note it's btu/h now)
New heat load = 1.085 * delta T * cfm
You know new heat load and cfm, so calculate new delta T.
Delta T = room temp  discharge air temp. You know discharge air temp, so you should be able to calculate room temp.
What is room temp? It would be the new steady state condition assuming constant discharge air temp and constant heat load.
In reality, your heat load will vary to some degree, your discharge air temp will vary (mind you, it will vary based on return air conditions, likely, and by adding this heat to the room you are likely changing return air conditions), your cfm might vary, the heat load figure you quoted probably isn't totally accurate, etc etc.
Point being, there isn't a real straightforward way to answer your question given the info you've presented, and even with additional info, you can calculate a number quickly on paper that will be a reasonably accurate approximation but will not be exact.

Yes you are correct I units should be BTU/hr.
My problem is the space is pretty complex. I have an industrial area with hundreds of piece of equipment. The volume I specified was for the local project area within the grander scheme of things.
Because of this:
I do not know the cfm without having an air balance done on the entire area, even then I do not know distribution.
Total heat load at this point would be nearly impossible to get and even if available would be overengineering the project I am currently working on.
Current temp of the room varies depending on season, equipment load factors, etc.
I suppose I was trying to figure out a method of determining what the addition of 70000 btu/hr would do to my local project area. The reason for this is I do not want to set off heat sensors to sprinkler heads should the air distribution not be adequate to dissipate the heat.
Given that it is not a straight forward answer I'm thinking maybe the best way to go about it is to incorporate some kind of high ambient safety shut off in the project area.
thank you for taking the time to respond

Well, on one hand, if you hadd 70,000 btu/hr of heat load, you can add 70,000 btu/hr of cooling to maintain the same temperatures.
It also sounds like the addition of air moving equipment (like ceiling mounted, low speed high velocity fans) might help your situation. Circulating the air could help avoid "hot spots" and might be a good way to approach your particular problem.
Generally speaking, you are asking a question that requires a lot of information to accurately answer. You can always just try it, and find out what happens...

Originally Posted by Garasaki
The solution is not as simple as you'd think.
The way you have phrased the question, you have a room sitting there at X degrees.
Then you add 70,000 btu/h (I assume you mean btu/h, rather then btu, since you mention it's running continuously).
So you say you are constantly adding heat. This means the temp will continue to rise. You make no mention of a way to dissipate the heat or remove the heat (ie cool...) from the room. Essentially, the answer to the question as you've phrased it is that after a very long time, the room will become the same temperature as the hottest surface of the equipment you placed in the room.
This is probably not what you mean.
You either want to know how much the room temp will rise due to a certain discrete addition of heat (ie you have a room, and then you add 70,000 btu (note, not btu/h) to it). This is fairly straight forward, as you could calculate the heat capacity of the air (based on a constant multiplied by the mass of the air in the room). Then it'd be heat added * heat capacity = temperature rise.
What you probably mean is how hot will the room become if you have some source of cooling in the room (where you know the CFM and the discharge temp), and then you add this piece of equipment.
You reference the good ole sensible heat equation. I guess we can assume you are only adding sensible heat (boy it's a lot easier that way...).
Heat = 1.085 * delta T * cfm
You need to start by considering the room before you add the equipment. You will need to know the current temp of the room, the cooling discharge air temp, and the cfm. You can then calculate the current heat load of the room.
Your new heat load = current heat load + 70,000 btu/h (again note it's btu/h now)
New heat load = 1.085 * delta T * cfm
You know new heat load and cfm, so calculate new delta T.
Delta T = room temp  discharge air temp. You know discharge air temp, so you should be able to calculate room temp.
What is room temp? It would be the new steady state condition assuming constant discharge air temp and constant heat load.
In reality, your heat load will vary to some degree, your discharge air temp will vary (mind you, it will vary based on return air conditions, likely, and by adding this heat to the room you are likely changing return air conditions), your cfm might vary, the heat load figure you quoted probably isn't totally accurate, etc etc.
Point being, there isn't a real straightforward way to answer your question given the info you've presented, and even with additional info, you can calculate a number quickly on paper that will be a reasonably accurate approximation but will not be exact.
great post
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