Answered: A piston-cylinder device initially…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A piston-cylinder device initially contains CO₂ at 200 kPa and 400°C and the total enclosed volume is 300 litres. Due to heat loss, the piston moves downwards to a position where it sits on a pair of stoppers and its final enclosed volume is 150 litres. Further heat loss leads to the pressure being reduced to 160kPa.

Workout 1) the final temperature, 2) the total work done by CO₂ and 3) the total heat transferred to CO₂. Also make some comments on the result of heat.

4) Create a schematic p-v diagram of the process

The following assumptions are to be made:

CO2 is a perfect gas and its molecular mass is 44kg/kmol.
The ratio of specific heat capacities, γ (gamma) is 1.3
The volume occupied by the stoppers is to be ignored.
There is no leakage in the system
There is no friction between the cylinder and piston walls and the piston moved slowly at the same speed therefore, no acceleration.
For the conversion from Celsius to Kelvin, use 273
Use 8314.5 J/kmol.K for the universal gas constant

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Follow-up Questions

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Follow-up Question

In the follow up question you have worked out the total work done ON CO2 and total heat transferred FROM CO2 but I asked to workout the total work done BY the CO2 and total heat transferred TO the CO2. Please clarify this, I am having to wait for so long with the answers to follow up questions, please reply quickly.

Answers:
1) The final temperature is 269.2 K
2) The total work done on the CO2 is 30 kJ
3) The total heat transferred from the CO2 is 150 kJ
4) Schematic p-v diagram of the process is

Solution

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Follow-up Question

I asked bartleby to solve this question earlier, it gave me AI answer which is completely different to what's shown in this answer. I don't know which one is correct now. I have attached screenshots of the AI answer. Can you clarify which is correct. Also I previously asked about pv diagram and you said ' the curve in the explanation is correct', did you mean in your explanation or the one I showed as an example? Please advice

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Step 5
The total heat transferred to CO2 can be calculated using the first law of thermodynamics, which states that
the change in internal energy is equal to the heat added to the system minus the work done by the system.
The change in internal energy can be calculated using the formula AU = n*Cv*(T2-T1), where n is the number
of moles, Cv is the specific heat at constant volume, and T2 and T1 are the final and initial temperatures
respectively. The number of moles can be calculated using the ideal gas law, which is P1*V1 = n*R*T1.
Substituting the given values, we get n = (200*10^3*300) / (8314.5*673) = 8.5 kmol. The specific heat at
constant volume Cv can be calculated using the formula Cv = R / (y-1), which gives Cv = 8314.5 / (1.3-1) =
20786.25 J/kmol.K. Substituting these values into the formula for change in internal energy, we get AU =
8.5*20786.25*(828.8-673) = 27.2*10^6 J. Therefore, the total heat transferred to CO2 is Q = AU+W=
27.2*10^6 + 75*10^6 = 102.2*10^6 J.
Step 6
In conclusion, the final temperature is 828.8 K, the total work done by CO2 is 75*10^6 J, and the total heat
transferred to CO2 is 102.2*10^6 J. The heat loss resulted in a decrease in pressure and volume, and an
increase in temperature. The p-v diagram of the process would show an initial decrease in volume with
constant pressure, followed by a decrease in pressure with constant volume.
Solution
The final temperature of the CO2 in the piston-cylinder device is 828.8 K. The total work done by the CO2 is
75*10^6 J and the total heat transferred to the CO2 is 102.2*10^6 J. The process involved heat loss, which
resulted in a decrease in pressure and volume, and an increase in temperature.

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Step 1
The objective of the question is to find the final temperature, total work done by CO2, and the total heat
transferred to CO2 in a piston-cylinder device. The process involves heat loss and volume reduction due to
the movement of the piston.
Step 2
First, we need to convert the initial temperature from Celsius to Kelvin. The initial temperature T1 in Kelvin
is 400°C + 273 = 673 K.
Step 3
Next, we calculate the final temperature. Since the volume is halved and the gas is perfect, we can use the
adiabatic process equation, which is T1*V1^(y-1) = T2*V2^(y-1). Substituting the given values, we get 673*
(300)^(1.3-1) = T2*(150)^(1.3-1). Solving for T2, we get T2 = 673* (300/150)^(1.3-1) = 673*2^0.3 = 673*1.231 =
828.8 K.
Step 4
The total work done by CO2 can be calculated using the formula for work done in an adiabatic process,
which is W = P1*V1 - P2*V2 / y-1. Substituting the given values, we get W = (200*10^3*300 - 160*10^3*150) /
(1.3-1)=75*10^6 J.

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Follow-up Question

The p-v diagram doesn't make sense. Can you double check that it's correct? Does it not have any curves in it as the ones in the image attached?

Solution

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