A system conducts 110 cal of heat to the surroundings while delivering 474 cal of work. What is the change in internal energy of the system(in cal)?
The correct answer and explanation is:
The change in internal energy of the system can be calculated using the first law of thermodynamics: ΔU=Q−W\Delta U = Q – W
Where:
- ΔU\Delta U is the change in internal energy,
- QQ is the heat added to or taken out of the system, and
- WW is the work done by or on the system.
In this case:
- The system conducts 110 cal of heat to the surroundings, so Q=−110 calQ = -110 \, \text{cal} (since heat is leaving the system, it is negative).
- The system delivers 474 cal of work, so W=474 calW = 474 \, \text{cal} (since work is done by the system, it is positive).
Now, applying the values into the equation: ΔU=(−110 cal)−(474 cal)\Delta U = (-110 \, \text{cal}) – (474 \, \text{cal}) ΔU=−110 cal−474 cal\Delta U = -110 \, \text{cal} – 474 \, \text{cal} ΔU=−584 cal\Delta U = -584 \, \text{cal}
Thus, the change in internal energy of the system is −584 cal-584 \, \text{cal}.
Explanation:
The first law of thermodynamics states that the change in the internal energy of a system is the sum of the heat added to the system and the work done by the system. In this case, the heat conducted out of the system decreases its internal energy, and the work done by the system further reduces the internal energy. Therefore, both the heat lost and the work done result in a decrease in the system’s internal energy, which is reflected in the negative value of −584 cal-584 \, \text{cal}. This means that the internal energy of the system has decreased by 584 cal.