A system gains 473J of kinetic energy while losing 271J of potential energy. The thermal energy increases by 127J .
Use an energy bar chart of this process to find the external work Wext.
To find the external work (Wext) in this process, we need to use the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred or transformed.
An energy bar chart is a visual representation of the different forms of energy involved in a process. It shows the initial and final energies of the system, as well as any energy transfers or transformations that occur. In this case, we have a system that gains kinetic energy, loses potential energy, and has an increase in thermal energy.
Let's break down the energy transfers and transformations in this process:
1. Kinetic Energy (KE): The system gains 473J of kinetic energy. This means that the initial kinetic energy of the system must have been lower than its final kinetic energy. So, we can represent the change in kinetic energy as follows:
Initial KE + 473J = Final KE
2. Potential Energy (PE): The system loses 271J of potential energy. This indicates that the initial potential energy of the system must have been higher than its final potential energy. We can represent the change in potential energy as:
Initial PE - 271J = Final PE
3. Thermal Energy (Q): The thermal energy of the system increases by 127J. Thermal energy represents the energy associated with the random motion of particles within the system. We can represent this as:
Initial Q + 127J = Final Q
Now, let's solve for the external work (Wext) using the conservation of energy:
According to the conservation of energy principle, the sum of all energies in the system remains constant. Therefore, the total change in energy of the system must be zero:
Change in KE + Change in PE + Change in Q + Wext = 0
Substituting the given values:
473J - 271J + 127J + Wext = 0
Combine like terms:
329J + Wext = 0
Solving for Wext:
Wext = -329J
Therefore, the external work (Wext) in this process is -329J, indicating that work is done on the system. The negative sign implies that work is done on the system, which means external forces are acting on the system to increase its energy.
To find the external work (Wext) using an energy bar chart, we need to account for the changes in different forms of energy. The equation for the energy bar chart is:
Initial energy + energy added - energy lost = final energy
Let's break down the given information:
- The system gains 473J of kinetic energy
- The system loses 271J of potential energy
- The thermal energy increases by 127J
Let's denote the external work as Wext. We can represent the energy changes in the energy bar chart as follows:
Initial energy (Ei) + Wext + Energy added (Ea) - Energy lost (El) = Final energy (Ef)
Plugging in the values, we get:
Ei + Wext + 473J - 271J = Ef
Since the system gains kinetic energy (Ea), we have:
Ea = 473J
Similarly, since the system loses potential energy (El), we have:
El = -271J
And the change in thermal energy is given as:
ΔEth = 127J
Now we can rewrite the equation as:
Ei + Wext + Ea + El = Ef
Substituting the known values:
Ei + Wext + 473J - 271J = Ef
Now we need to express the initial energy (Ei) and final energy (Ef) in terms of the changes in different forms of energy:
Ei = Ea + El + Eth = 473J - 271J + ΔEth
Ef = Ea + Eth
Substituting these values into the equation:
(Ea + El + ΔEth) + Wext + Ea + El = Ea + Eth
Simplifying the equation:
2Ea + 2El + ΔEth + Wext = Eth
Since the external work (Wext) is the only unknown, we isolate it:
Wext = Eth - 2Ea - 2El - ΔEth
Plugging in the values:
Wext = 127J - 2(473J) - 2(-271J) - 127J
Calculating this expression:
Wext = 127J - 946J + 542J - 127J
Wext = -404J
Therefore, the external work (Wext) is -404J.