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.
 A: First of all, the temperature of a room at its size are not intrinsically related.
If you let any room thermally equilibrate with its environment, it will have the same temperature as the environment, no matter its size.
This is more or less the definition of thermal equilibrium and temperature:
If you bring two objects in thermal contact with each other, their temperatures will become the same over time (assuming no further heat sources or sinks).
Now, a room or building in summer is usually not in thermal equilibrium:

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*The temperature of the environment changes over the day, with the room usually lagging behind.

*Buildings, the ground, etc. are a big retainer of heat or cold.
It can take months of summer to heat up a building (and the ground it’s standing on) to outside air temperatures (on the daily average).
This is roughly the reason why the hottest months of the year follow the summer solstice instead of being centred around it.

*The room is usually subject to the literal greenhouse effect:
Heat comes in via solar radiation and then is constrained due to lack of ventilation.

*The room may contain heat-producing entities such as humans, cooking devices, computers, etc.

With all that in mind, here are a few effects that why big room tend to be cooler (or seem cooler) during summer:

*

*A bigger room has less surface per volume.
Surface is bad because this is how the heat comes in, either via solar radiation or thermal exchange with the outside.
Volume is good, because it retains cold, in particular in form of stuff.

*In a big room, hot air can float up so the inhabitants don’t notice it, even if the room is as hot as a smaller room on average.

*Bigger rooms tend to contain fewer heat-producing entities per volume.

*Bigger rooms are easier to ventilate, in particular using the chimney effect.

*In bigger rooms, you have more air flow due to convection (not only the chimney effect).
This in turn reduces the apparent temperature (just like fans).

*Bigger rooms tend to require thicker walls to support them, which in turn tend to isolate better (and also store cold).

A: 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 
A: 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). 
A: 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.
