Question

An office room contains about $2000$ moles of air. The change in the internal energy of this much air when it is cooled from ${34}^{o}C$ to ${24}^{o}C$ at a constant pressure of $1.0$ atm is
(Use ${\gamma }_{aor}=1.4$ at universal gas constant $=8,314J/molK$)

• A. $-1.9\times {10}^{5}J$
• B. $+1.9\times {10}^{5}J$
• C. $-4.2\times {10}^{5}J$
• D. $+0.7\times {10}^{5}J$

Answer 1

The correct option is C $-4.2\times {10}^{5}J$

Change in internal energy $dU=n{C}_{v}dT$
Given : $n=2000$ $dT=24-34=-{10}^{o}C$
Also, $C_v=\frac{R}{\gamma -1}=\frac{R}{1.4-1}=\frac{R}{0.4}=\frac{8314}{0.4}$
$dU=2\times {10}^3\times \frac{8314}{0.4}(-10)=-4.2\times {10}^5$