I have to find final temperature of water in an heat exchanger.
the heat exchanger must cool down air using water, meaning initial temperature of water must be cold,
initial temperature of air is 298.15 Kelvin
I can use this equation to find initial temperature of water, $Q_{max} = C_{min}*\delta T$ where $C_{min} = \frac{kg}{s} * \frac{J}{kg*K} = \frac{W}{K}$
and this is not a problem, but here comes my question: in order to find final temperature from this equation $T_{out, water} = T_{in, water} +/- \frac{Q}{C}$
how can I know which sign to plug into this equation?
this is my reasoning, let me know if it's right: if the text says water is cooling down air, that means initial temperature of water is becoming warmer than before by taking heat from air (i.e the hot fluid), and therefore equation becomes: $T_{out, water} = T_{in_water} + \frac{Q}{C}$
if this is true, then minus sign means the contrary.
but sometimes I have an exercise that say the same thing, but it requires me to flip the signs, for example, "air is being extracted from a server room and it has to be cooled down by cold water", in this case, exercise requires to use this equation: $T_{out, water} = T_{in_water} - \frac{Q}{C}$ so I think my reasoning is wrong or at least it cannot be applied all the time for every situation.