# Relation between volume of a room and temperature inside

I don't know whether it is based on some people's assumptions or it is a fact that the smaller the room, the hotter it is (say, during summer), considering the heat is only supplied from outside the room. I am wondering if there is any relation between the volume of a room and the temperature. If it is so, is there equation that can explain that relation? I only know the equation that explains the relation between temperature, volume, and pressure for only ideal gas.

Thank you.

Temperature, like pressure, is an intensive thermodynamic property of a system, meaning it is independent of the mass of a system. If the temperature of a room is 300K if the room is divided in half the temperature of each half is also 300K.

Properties like internal energy and entropy are extensive properties meaning they depend on the mass of the system. In order to differentiate the internal energy per unit mass from the total internal energy of a system a lower case $$u$$ is used vs upper case $$U$$. The lower case is then referred to as the specific internal energy.

The temperature of the air of a smaller room will increase more rapidly in the summer than a larger room because there is less air to transfer heat to from outside. It also takes less time to cool a smaller room because there is less air to transfer heat out of.

Hope this helps

• Thank you, it's likely related to temperature gradient, right. I am thinking that it's about the way the heat transfers, for example by convection Mar 10 '20 at 23:09
• @elluthfi You are right. The rate of heat transfer is definitely proportional to the temperature gradient, all other things being equal. Mar 12 '20 at 0:23

No there is no relationship between temperature and volume of the room, because the temperature of the room depends on the temperature of the surrounding. For example the temperature of of a iron rod placed in a furnace is the same as that of furnace (under thermal equilibrium).

But there is one advantage of room with greater volume which is that a room with greater volume requires greater time to heat up to a given temperature than one with smaller volume (assuming that other conditions remain the same).

• Thanks, so it's more or less related to temperature gradient, isn't it? Mar 10 '20 at 23:07

If it is an apartment in a building, I don't see any effect. But in a house, where a great part of the heat input comes from the roof heated by the sun, it makes a difference.

There is a gradient of temperature from the roof to the ground.

Of course opened windows help to exchange the superheated top layers, but it also helps if that layers are 6m above us instead of 3m for example.

• That's what is likely to occur, thank you Mar 10 '20 at 23:10