Why is solar radiation equal to long wavelength emission?

[aldo sebastian]

In my heat transfer course, I always had to do analysis of long-wavelength radiation between surfaces first, and find the heat radiated from one of the surface. Then, solar radiation is added to the problem, and suddenly it was said that solar radiation=heat radiated from this surface! Does anyone know why we take solar radiation to be equal to long wave radiation emission?

 

[CWatters]

Perhaps because it's reached thermal equilibrium eg temperature has stopped rising. Under that condition power in = power out.

 

[aldo sebastian]

Perhaps because it's reached thermal equilibrium eg temperature has stopped rising. Under that condition power in = power out.

But then now the solar radiation adds energy to the system; shouldn’t the emission increase because now it receives more radiation than before? i.e. the solar radiation adds more energy to the surface than before, and thus should increase its temperature more, and thus its emission?

 

[CWatters]

Yes, if solar gain increases then the temperature will rise and it will radiate more.

While temperature is rising solar gain > radiated loss.

When temperature is stable solar gain = radiated loss. The exact amount of gain/loss depends on the temperature and other factors.

While temperature is falling solar gain < radiated loss.Consider a house in winter. If you set the thermostat to 18C the house will eventually reach 18C. When its stable at 18C the power going into the house will be equal to the power lost through the walls. Let's say they are both 10kW.

If you turn up the thermostat to 20C the heating system will increase its output delivering more heat than the house is loosing and the temperature will rise and the losses increase.

Once the temperature is stable at 20C the power going into the house will again be equal to the power lost. However the loss will be greater because the temperature gradient through the wall will be higher. They might both be 11kW.