# Temperature change (first law of thermodynamics)

• I
Hi,

From the first law of thermodynamics it follows:

Cp * (δT/δt) = (δQ/δt)
where Cp = specific heat capacity, T = temperature, Q = heat, t = time

From this formula, you would derive that temperature keeps on increasing as long as dQ/dt > 0. But if you, for example, look at the idealized diurnal evolution of air temperature, it can be seen that the temperature keeps on increasing until its maximum value, despite the fact that there is net heat loss (dQ/dt < 0 for example between noon and 4h where the area between both curves becomes smaller)...

It seems that on the figure here the temperature keeps on rising as long as the value of Q itself > 0 but that doesn't necessarily mean that dQ/dt has to be > 0, right? Is my reasoning wrong or how can this correctly be explained with formulas?

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russ_watters
Mentor
The sun doesn't heat the air, it heats the ground.

Chestermiller
Mentor
Hi,

From the first law of thermodynamics it follows:

Cp * (δT/δt) = (δQ/δt)
where Cp = specific heat capacity, T = temperature, Q = heat, t = time

From this formula, you would derive that temperature keeps on increasing as long as dQ/dt > 0. But if you, for example, look at the idealized diurnal evolution of air temperature, it can be seen that the temperature keeps on increasing until its maximum value, despite the fact that there is net heat loss (dQ/dt < 0 for example between noon and 4h where the area between both curves becomes smaller)...

It seems that on the figure here the temperature keeps on rising as long as the value of Q itself > 0 but that doesn't necessarily mean that dQ/dt has to be > 0, right? Is my reasoning wrong or how can this correctly be explained with formulas?

View attachment 205308
dQ/dt is the current rate of solar heat flow. So throughout the day, current rate of solar heat flow is positive. The graph says Energy Rate, not cumulative amount of energy.

russ_watters
dQ/dt is the current rate of solar heat flow. So throughout the day, current rate of solar heat flow is positive. The graph says Energy Rate, not cumulative amount of energy.
Oh I get it,

it's just that the temperature change is Eulerian (a local change at a fixed position) whereas the energy flux density is Lagrangian (it crosses the air on its path while having a negative or positive value).

Chestermiller
Mentor
Oh I get it,

it's just that the temperature change is Eulerian (a local change at a fixed position) whereas the energy flux density is Lagrangian (it crosses the air on its path while having a negative or positive value).
Both are as reckoned by a "stationary" observer on the surface of the earth.