If an air cooler cools at a rate of T1 C/s and a heater heats at a rate of T2 C/s where T1=T2. Assume, the heater is placed in the same environment as the air cooler. Then, will the temperature of the system increase or decrease.
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Both the individual systems (i.e) the heater and the air cooler produce heat during work which affect the environment. So, the combined system has a net increased temperature due to the two systems.
The prevailing temperature of the atmosphere along with the added temperature of the heater forces the temperature to increase exponentially beyond the rate of heating of the heater.