FIGURE: h t t p : / / g o o . g l / a 7 j C F
The figure is a PV diagram for a reversible heat engine in which 1.0 mol of argon, a nearly ideal monatomic gas, is initially at STP (point a). Points b and c are on an isotherm at T = 423 K. Process ab is at constant volume, process ac at constant pressure.
What is the efficiency of this engine?
To determine the efficiency of the engine, we need to use the definition of efficiency for a heat engine:
Efficiency = (Net work output / Heat input)
In this case, the net work output is equal to the area enclosed by the closed loop on the PV diagram, and the heat input can be determined by the heat added during process ab.
Let's break down the steps to determine the efficiency:
Step 1: Determine the work done during process ab.
- Since process ab is at constant volume, there is no work done during this process. Therefore, the work done during this step is zero.
Step 2: Determine the heat added during process ab.
- By the first law of thermodynamics, for a constant volume process, the change in internal energy (ΔU) is equal to the heat added (Q). Therefore:
Q = ΔU
- Since argon is a monatomic ideal gas, the change in internal energy can be determined using the equation:
ΔU = (3/2)nR(Tf - Ti)
where n is the number of moles of gas, R is the ideal gas constant, Tf is the final temperature, and Ti is the initial temperature.
- In this case, n = 1.0 mol, R = 8.314 J/(mol K), Tf = 423 K, and Ti = 273 K.
Calculate ΔU using the above equation.
Step 3: Determine the heat input during process ac.
- Since process ac is at constant pressure, the heat input (Qin) can be determined using the equation:
Qin = nCp(Tc - Tb)
where n is the number of moles of gas, Cp is the heat capacity at constant pressure, Tc is the final temperature, and Tb is the initial temperature.
- In this case, n = 1.0 mol, Cp for monatomic ideal gas = 3/2R, Tb = 273 K, and Tc = 423 K.
Calculate Qin using the above equation.
Step 4: Determine the net work output.
- The net work output is equal to the area enclosed by the process path on the PV diagram.
- Calculate the area enclosed by the loop on the PV diagram using the given values.
- If the area is positive, it represents work done by the system. If the area is negative, it represents work done on the system.
Step 5: Calculate the efficiency.
- Substitute the values for net work output and heat input into the efficiency formula and calculate the result.
Note: Since you provided a shortened URL for the figure, I cannot directly access it. However, the above steps can be followed based on the provided information about the processes on the PV diagram.
By following these steps, you should be able to determine the efficiency of the engine.