Thermodynamics / Q = mC⌂T equation in air application

In summary, to prevent the temperature inside a radio equipment cabin from rising more than 15°C above the outside temperature, one must circulate enough 'free air' per hour to absorb the 15kW heat load. This can be determined using the equation Q = mC⌂T, where C = 1.007 and ⌂T = -15. The ideal gas law, pV = nRT, can also be used as a substitute. However, it is important to make accurate assumptions for temperature and pressure. Alternatively, one can calculate the amount of air mass needed to remove all the heat generated by the equipment in an hour."
  • #1
Phystudent91
6
0

Homework Statement



If you have a radio equipment cabin that has a heat load of 15kW and you wish to stop the temperature becoming more than 15°C hotter than outside, how much 'free air' (outside/atmospheric air) needs to be circulated inside the cabin per hour?


Homework Equations



Q = mC⌂T
C = 1.007
⌂T = -15

The Attempt at a Solution



I don't know how to relate the m (usually a mass, right?) to a volume of air, as I assume that is the equations equivalent.
I hope that makes sense...
 
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  • #2
There is an ideal gas law saying pV = nRT which is good enough for this kind of thing. You'll have to make a decent assumption for T and p (p is easy, T is more vague).
But: what's against answering soandsomany kilograms per hour if they ask "how much" ?
 
  • #3
Let m be the amount of air mass that passes through the room in an hour. How much heat does it have to absorb in an hour to remove all the heat generated by the radio equipment?

Chet
 

1. What is the Q = mC⌂T equation in air application used for?

The Q = mC⌂T equation, also known as the specific heat equation, is used to calculate the amount of heat transferred in a system when there is a change in temperature. In air applications, this equation is commonly used to determine the amount of heat required to change the temperature of a specific amount of air.

2. What do the variables in the Q = mC⌂T equation represent?

The Q represents the amount of heat transferred, measured in joules (J). The m represents the mass of the substance, measured in kilograms (kg). The C represents the specific heat capacity of the substance, measured in joules per kilogram per degree Celsius (J/kg°C). The ⌂T (delta T) represents the change in temperature, measured in degrees Celsius (°C).

3. How is the Q = mC⌂T equation derived?

The Q = mC⌂T equation is derived from the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred. This equation specifically relates to the transfer of heat energy, and is based on the concept that the amount of heat transferred is proportional to the mass of the substance, the specific heat of the substance, and the change in temperature.

4. Can the Q = mC⌂T equation be used for any substance?

Yes, the Q = mC⌂T equation can be used for any substance, as long as the specific heat capacity is known. However, it is important to note that the specific heat capacity can vary depending on the substance, so the equation may need to be adjusted accordingly.

5. How is the Q = mC⌂T equation applied in real-world situations?

The Q = mC⌂T equation is commonly used in various industries, such as HVAC (heating, ventilation, and air conditioning) and chemical engineering. It can be used to calculate the amount of heat required to heat or cool a specific volume of air, determine the capacity of heating or cooling systems, and design efficient heat exchange systems. It is also used in experiments and research to study the thermodynamic properties of different substances.

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