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We know that internal energy at a temperature

U=nC_vT

Where U=internal energy

n=number of moles

C_v=molar specific heat at constant volume

T=temperature

Air in home is chiefly diatomic molecules, so

C_v for diatomic moles is given as

So,

We know ideal gas equation

PV=nRT

Where V= volume of gas

R=gas constant=8.31Jmol^-1K^-1

T=temperature

n=number of moles of gas

P=pressure of gas

Substituting the value of nRT from ideal gas equation to U

Now, it is given in question that pressure remains constant throughout the day and volume V of room is also constant. So, PV is a constant.

Hence U is also constant.