Show that the internal energy of the air (treated as an ideal gas) contained in a room remains constant as the temperature changes between day and night. Assume that the atmospheric around remains constant and the air in the room maintains this pressure by communicating with the surrounding through the windows etc.

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Solution

During day the temperature increases
During night, the temperature decreases.
But $P V$ =constant.
$P V = n R T = n T = \frac{P V}{R}$
Internal energy, $U = n R T$ =constant $\times R$ =constant.
$∴$ In the room, internal energy remains constant.

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During day the temperature increases During night, the temperature decreases.But PV=constant.PV=nRT=nT=PVRInternal energy,U=nRT=constant ×R=constant.∴ In the room, internal energy remains constant.

During day the temperature increases
During night, the temperature decreases.
But $P V$ =constant.
$P V = n R T = n T = \frac{P V}{R}$
Internal energy, $U = n R T$ =constant $\times R$ =constant.
$∴$ In the room, internal energy remains constant.