A heat engine carries 2.60 mol of an ideal monatomic gas around the cycle shown in the figure. Process 1-2 takes place at constant volume and takes the gas from 300 K to 600 K, process 2-3 is adiabatic and takes the gas from 600 K to 455 K, and process 3-1 takes place at a constant pressure and returns the gas to 300 K. Compute the heat Q for the whole cycle. Compute the change in internal energy DeltaE for the cycle as a whole.Calculate the work done by the gas for the cycle.If the initial pressure at point 1 is 1.4 atm, find the pressure at point 2 in atm. If the initial pressure at point 1 is 1.4 atm, find the volume at point 3 (in m3).
the figure....
To solve this problem, we need to use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
1. Compute the heat Q for the whole cycle:
We can use the equation Q = ΔE + W, where ΔE is the change in internal energy and W is the work done by the gas. Since the cycle is closed, the change in internal energy for the cycle as a whole is zero. Thus, Q = W.
2. Compute the change in internal energy ΔE for the cycle as a whole:
Since the cycle is closed, the change in internal energy for the cycle as a whole is zero. Therefore, ΔE = 0.
3. Calculate the work done by the gas for the cycle:
The work done by the gas can be calculated using the equation W = ∫PdV, where P is the pressure and V is the volume. Since process 1-2 occurs at constant volume, the work done during this process is zero. For process 2-3, we're given that it is adiabatic, meaning there is no heat exchange and the work done is also zero. Finally, process 3-1 occurs at constant pressure. Therefore, we can use the equation W = PΔV, where ΔV is the change in volume. We need to find the volume at points 1, 2, and 3 to calculate this.
4. Find the pressure at point 2:
We're given that the initial pressure at point 1 is 1.4 atm. Since process 1-2 happens at constant volume, the pressure remains the same. Therefore, the pressure at point 2 is also 1.4 atm.
5. Find the volume at point 3:
Since process 3-1 happens at constant pressure, we can use the ideal gas law equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. We're given that the gas carries 2.60 mol and the initial pressure at point 1 is 1.4 atm. We can use this information to find the volume V1 at point 1. Then, we can use the same equation to find the volume V3 at point 3, given that the temperature is 300 K.
By following these steps, you should be able to calculate the heat Q for the whole cycle, the change in internal energy ΔE for the cycle as a whole, the work done by the gas for the cycle, the pressure at point 2, and the volume at point 3.