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# 1 mole of ideal monatomic gas at $27^{\circ}C$ expands adiabatically against a constant external pressure of $1.5\: atm$ from a volume of $4\: dm^3\: to\: 16\: dm^3$ . Calculate $\Delta E$.

$\begin {array} {1 1} (A)\;1823.85\: J & \quad (B)\;- 1823.85 \: J \\ (C)\;3039.75 \: J & \quad (D)\;-3039.75 \: J \end {array}$

Since the process is adiabatic, so, $q=0$
$W = -P (\Delta V) = -1.5 \times (V_2 – V_1) = -1.5(16-4)$
$= -18\: atm \; dm^3 = -18 \times 101.325 \: J = -1823.85 /j$
So, $\Delta E = q + W = 0 + (-1823.85) = -1823.85\: J$