Question

The internal energy of air in a room of volume 50 m${}^3$ at atmospheric pressure will be

• A. 2.5 X 10${}^7$ erg
• B. 2.5 X 10${}^7$ Joule
• C. 5.255 X 10${}^7$ Joule
• D. 1.25 X 10${}^7$ Joule

Answer 1

Answer: (D)

1.25 X 10${}^7$ Joule

The internal energy of the room is given by the molecular motion and is called as the kinetic internal energy given by $\frac{f}{2}nRT$. Using the gas law we have $PV=nRT$ and as the gas is mainly comprised of nitrogen and oxygen both being diatomic we take the degree of freedom as 5. Thus we calculate internal energy as $\frac{5}{2}PV=\frac{5}{2}\times 1.013\times {10}^5\times 50=1.25\times {10}^{7}J$