Answer:
[tex]\Delta Q=-230kJ[/tex]
Explanation:
Using the first law of thermodynamics:
[tex]\Delta U=\Delta Q-W[/tex]
Where [tex]\Delta U[/tex] is the change in the internal energy of the system, in this case [tex]\Delta U=250kJ[/tex], [tex]\Delta Q[/tex] is the heat tranferred, and [tex]W[/tex] is the work, [tex]W=-480kJ[/tex] with a negative sign since the work is done by the system.
From the previous equation we solve for heat, because it is the unknown variable in this problem
[tex]\Delta Q=\Delta U +W[/tex]
And replacing the known values:
[tex]\Delta Q=250kJ +(-480kJ)[/tex]
[tex]\Delta Q=250kJ -480kJ[/tex]
[tex]\Delta Q=-230kJ[/tex]
The negative sign shows us that the heat is tranferred from the system into the surroundings.