Respuesta :
Since the system itself is giving off heat, this is a reduction in the internal energy.
heat = - 25,000 J
Since work is being done on the system, therefore it is an additional energy to the system. Work is given as:
work = - P dV
work = - 1.50 atm (6 L – 12 L)
work = 9 L atm
Since it is given that 1 L atm is equivalent to 101.3 J, therefore the total energy added is:
energy due to work = 9 L atm (101.3 J / 1 L atm)
energy due to work = 911.7 J
Therefore the total change in internal energy is the sum of heat and energy due to work:
Change in internal energy = - 25,000 J + 911.7 J
Change in internal energy = - 24,088.3 J
Therefore, approximately 24.1 kJ of energy is lost by the system in the total process.
Answer:
-24.1 kJ
The correct option is d. which is the change in internal energy is -24.9 kj.
Given to us:
- Heat system is giving off, [tex]Q_{out}= -25000[/tex]
- Initial volume, [tex]V_{i}=12\ l[/tex]
- Final volume, [tex]V_{i}=6\ l[/tex]
- Pressure, [tex]P= 1.50\ atm[/tex]
- Also, a piece of additional information is given to us, [tex]101.3\ j = 1\ l\cdot atm[/tex].
Work
As work is being done on the system, meaning additional energy is provided to the system. Therefore,
[tex]\begin{aligned}W&=- \int\limits {P} \, dv\\&=-P\ dv\\\\&=-P\ (V_f-V_i)\\&=- (1.50) (6-12)\\&= 9\ l\cdot atm\end{aligned}[/tex]
Also,
[tex]1\ l\cdot atm=101.3\ j\\9\ l\cdot atm=101.3\times 9\\9\ l\cdot atm=911.7\ j[/tex]
According to the First law of thermodynamics,
[tex]\Delta U = Q - W\Delta\\\\where,\\ U = change\ in\ internal\ energy\\Q = heat\ added\\W = work\ done\ by\ the\ system[/tex]
Substituting the values,
[tex]\begin{aligned}\\\Delta U&= Q - W\Delta\\&= -25000+911.7\\&=-24,088.3\ j\\&= -24.0883\ kj\end{aligned}[/tex]
Hence, the change in internal energy is -24.0883 kj.
Learn more about First law of thermodynamics:
https://brainly.com/question/7107028
