Solve 1st Law of Thermo P20.38: Net Work & Energy

In summary, the conversation discusses an ideal gas taken through a cycle as shown in Figure P20.38. The net work done on the gas per cycle is given by the integral of pressure with respect to volume. For the processes AB and CD, the work done is zero as they are constant volume processes. The work done for process BC and DA is given by equations involving the initial pressure, volume, and the number of moles of gas. The net work done on the gas is the negative value of the sum of the work done for processes BC and DA.
  • #1
maxpowers_00
5
0
An ideal gas initially at Pi, Vi, and Ti is taken through a cycle as in Figure P20.38 (n = 2.6).

Figure P20.38 (see attachment)

(a) Find the net work done on the gas per cycle.
PiVi
(b) What is the net energy added by heat to the system per cycle?
PiVi
(c) Obtain a numerical value for the net work done per cycle for 1.15 mol of gas initially at 0°C.
kJ

a) i though at first that W= area of the cycle, which came out to be 6.76 but, it was wrong.

as for part b, i have no idea

c) W=nRTln(vi/2.6vi) = W=(1.15)(8.314)(273)ln(1/2.6) = 2.5kJ but this also turned out to be wrong

any ideas?

thanks
 

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  • #2
Work done is given by

[tex]W=\int_{V_1}^{v_2} PdV[/tex]

so clearly for process AB & CD W=0 as constant Volume Process

For BC : it would be WBC = nP0V0{n-1}
For DA : it would be WDA = -P0V0{n-1}

U can see net work done on the gas is the negative one so it is

W= -P0V0{n-1}

Net work done will be WBC + WDA
 
  • #3
for the response!

To find the net work done on the gas per cycle, we can 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. In this case, since the gas is an ideal gas, we can use the ideal gas law, PV=nRT, to solve for the change in internal energy and then use that to find the net work done.

a) The net work done on the gas per cycle can be found by calculating the area enclosed by the cycle in the PV diagram. From the diagram, we can see that the cycle consists of two parts - an isothermal expansion and an isobaric compression. The area under the isothermal curve represents the work done by the gas, while the area under the isobaric curve represents the work done on the gas. So, we can calculate the net work done as follows:

W = Work done by the gas - Work done on the gas
= (Area under isothermal curve) - (Area under isobaric curve)
= (nRTln(Vi/Vf)) - (PΔV)
= (2.6)(8.314)(273)ln(1/2.6) - (Pi)(Vi-Vi/2.6)
= -2.5kJ (since PiVi=PfVf)

b) The net energy added by heat to the system per cycle can be found by using the first law of thermodynamics again. From part a, we know that W = Q - (nRTln(Vi/Vf)). So, we can rearrange this equation to solve for Q:

Q = W + (nRTln(Vi/Vf))
= -2.5kJ + (2.6)(8.314)(273)ln(1/2.6)
= 2.5kJ

c) To find the net work done per cycle for 1.15 mol of gas initially at 0°C, we can substitute the given values into the equation from part a:

W = (nRTln(Vi/Vf)) - (PΔV)
= (1.15)(8.314)(273)ln(1/2.6) - (Pi)(Vi-Vi/2.6)
= -1.2kJ (since PiVi=PfVf)

So, the
 

1. What is the 1st law of thermodynamics?

The 1st law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another.

2. How is net work calculated in the 1st law of thermodynamics?

Net work is calculated by subtracting the work done by the system from the work done on the system. This can be represented as Wnet = Wsystem - Wsurroundings.

3. What is the relationship between net work and energy in the 1st law of thermodynamics?

The 1st law of thermodynamics states that the net work done on a system is equal to the change in the system's internal energy plus the heat transferred to the system. This can be represented as Wnet = ΔU + Q.

4. How is the 1st law of thermodynamics applied in real-world situations?

The 1st law of thermodynamics is applied in many real-world situations, such as in the design of engines, power plants, and refrigeration systems. It is also used in the study of energy conservation and renewable energy sources.

5. What is the significance of the 1st law of thermodynamics for understanding energy in our universe?

The 1st law of thermodynamics is crucial for understanding how energy behaves in our universe. It helps us understand that energy cannot be created or destroyed, only transformed, and that all energy systems must follow this fundamental law. It also plays a key role in the study of thermodynamics and energy conservation.

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