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 pressure around remains constant and the air in the room maintains this pressure by communicating with the surrounding through the windows, doors, etc.

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Solution

Internal energy = nRT

Now, PV = nRT

nT = PV

here P and V constant So, nT in constant

$∴$ Internal energy = R $\times$ constant

= constant

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Internal energy = nRT Now, PV = nRT nT = PV here P and V constant So, nT in constant ∴ Internal energy = R × constant = constant

Internal energy = nRT

Now, PV = nRT

nT = PV

here P and V constant So, nT in constant

$∴$ Internal energy = R $\times$ constant

= constant