The internal energy of air in a 4 m times 4 | vedclass

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(B) The internal energy $U$ of an ideal gas is given by $U = n C_v T$. For a diatomic gas,the degrees of freedom $f = 5$,so $C_v = \frac{fR}{2} = \fra

Vedclass · Accepted Answer

$12$

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(B) The internal energy $U$ of an ideal gas is given by $U = n C_v T$. For a diatomic gas,the degrees of freedom $f = 5$,so $C_v = \frac{fR}{2} = \frac{5R}{2}$. Substituting this into the internal energy equation: $U = n \left( \frac{5R}{2} ight) T = \frac{5}{2} nRT$. Using the ideal gas law $PV = nRT$,we can substitute $nRT$ with $PV$: $U = \frac{5}{2} PV$. Given: Pressure $P = 1 	ext{ atm} \approx 10^5 	ext{ Pa}$,Volume $V = 4 	imes 4 	imes 3 = 48 	ext{ m}^3$. Calculating $U$: $U = \frac{5}{2} 	imes 10^5 	imes 48 = 5 	imes 10^5 	imes 24 = 120 	imes 10^5 	ext{ J} = 12 	imes 10^6 	ext{ J}$.

The internal energy of air in a $4 \ m \times 4 \ m \times 3 \ m$ sized room at $1$ atmospheric pressure will be . . . . . . $\times 10^6 \ J$. (Consider air as a diatomic molecule)

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