Question

consider a system of gases that is compressed using 986 j from a piston, while losing 362 j of heat to the surroundings. what is the change in energy of this system?
+1348j
+624j
-624j
-1348j

Explanation:

Step1: Recall First Law of Thermodynamics

The first law of thermodynamics is $\Delta U = Q + W$, where $\Delta U$ is the change in internal energy of the system, $Q$ is the heat transferred, and $W$ is the work done on or by the system. When the system loses heat, $Q$ is negative; when work is done on the system, $W$ is positive.

Step2: Identify Values of Q and W

• Work done on the system ($W$): The system is compressed, so work is done on it. Thus, $W = + 986\,\text{J}$.
• Heat transferred ($Q$): The system loses heat to the surroundings, so $Q = - 362\,\text{J}$ (wait, no, wait the numbers: wait the problem says "losing 362 J"? Wait no, looking back: the problem says "compressed using 986 J" (work done on system, $W = + 986$) and "losing 362 J of heat"? Wait no, maybe a typo? Wait the options have 1348, 624, etc. Wait maybe the heat loss is 3622? Wait the image: "losing 3622 J of heat". Oh, I misread. So $Q = - 3622\,\text{J}$ (since heat is lost by the system), $W = + 986\,\text{J}$ (work done on the system).

Step3: Calculate $\Delta U$

Using $\Delta U = Q + W$, substitute the values:
$\Delta U = (- 3622\,\text{J}) + (986\,\text{J})$
$\Delta U = - 3622 + 986 = - 2636$? Wait no, that's not matching options. Wait maybe I mixed up $Q$ and $W$? Wait no, maybe the work is done by the system? No, compression: work is done on the system. Wait the options: +1348, +624, -624, -1348. Wait maybe the heat loss is 362 J? Wait no, the image: "losing 3622 J"? Wait no, maybe the numbers are 986 and 362? Wait no, the options are 1348, 624, etc. Wait maybe I made a mistake. Wait let's re-express:

Wait maybe the heat is $Q = - 362\,\text{J}$ (losing 362 J) and work $W = + 986\,\text{J}$. Then $\Delta U = - 362 + 986 = 624\,\text{J}$? No, that's +624. Wait but the options have +624. Wait maybe the heat loss is 362 J, not 3622. Maybe a typo in the problem. So assuming $Q = - 362\,\text{J}$ (losing 362 J) and $W = + 986\,\text{J}$ (work done on system). Then $\Delta U = Q + W = - 362 + 986 = 624\,\text{J}$? Wait no, 986 - 362 = 624. Wait but the options have +624. Wait maybe the heat is 3622? No, 986 - 3622 = -2636, not in options. So maybe the work is done by the system? No, compression: work done on system. Wait maybe the problem is: the system is compressed (work done on system, $W = + 986$) and gains heat? No, it's losing. Wait the options: +1348, +624, -624, -1348. Let's check: 986 - 362 = 624? No, 986 + 362 = 1348? Wait if $Q$ is positive (heat gained), but the system is losing heat. Wait maybe the sign convention: when heat is lost by the system, $Q$ is negative; work done on the system, $W$ is positive. So $\Delta U = Q + W$. If $W = 986$, $Q = - 362$, then $\Delta U = 986 - 362 = 624$. So +624 J.

Answer:

+624 J (the option with +624 J)