Answer
$\Delta E = 1474J$ $\Delta H = 824J$
Work Step by Step
First we find $\Delta E$ since $\Delta E = q + w $. We are told that the gas absorbs 824J of heat from the surroundings. Since the heat is absorbed (enters the system), the value of q = + 824J. Then we are told that 0.65 kJ of P-V work is done on the system. Since the work is done on the system (energy enters the system) we have w = + 0.65 kJ = + 650 J. Then we have $\Delta E = 824J + 650J = 1474 J$ Then we know that $\Delta H = \Delta E + P\Delta V$ Since the work done in the expansion or compression of a gas is $w =- P\Delta V$ so if we have w = +650 then $-P\Delta V = 650J$ so then $P\Delta V = -650J$ Then we have $\Delta H = 1474J - 650J = 824J$
