Question

A system has internal energy equal to $U$ $600J$ of work done on the system when $450J$ of heat is lost. The final energy of the system is:

• A. $U_1+150$
• B. $U_1+1050$
• C. $U_1-150$
• D. none of the above

Answer 1

Answer: (A)

$U_1+150$

Change in internal energy $=$ heat supplied $+$ work done

$\Delta U=q+w$
As per sign convention, work done on the system by the surrounding has positive sign and the heat released from the system to the surrounding has a negative sign.
Hence, $w=600$ J and $q=-450$ J

Substituting values in the expression for the change in internal energy, we get
$\Delta U=q+w=-450+600=150$ J
This is approximately equal to $120$ J.

Let the final energy of the system be $E_2$.
However, the change in internal energy, $\Delta U=E_2-E_1$
Hence, $E_2=(E_1+150)$ J

Therefore, the final energy of the system is $(E_1+150)$ J.