How much heat is transferred during the compression?

In summary: How much heat is transferred in this second increase in pressure?The Work involved that you (Doc Al) mentioned was in fact the third of four questions asked. Here it is.W = \int_{P_i}^{P_f} VkP dP = \frac{1}{2} V k P^2_f\frac{1}{2}(5.58X10^{-5}m^3)(6.18X10^-^1^2Pa^{-1})(5.07X10^8Pa)^2= 51.7N-m =51.7
  • #1
rsd_sosu
4
0
Would Someone check my work please?
Here is the question.
The pressure on 500g of copper is increased reversibly and isothermally from 0 to 5000atm.
Where
density = 8.96X10^3kg/m^3
Volume Expansivity = 49.5X10^-6K^-1
isothermal compressibility = 6.18X10^-12Pa^-1
specific heat = 385 J/Kg*K
temp = 298K

Now the first part of the question ask how much heat is transferred during the compression? (I worked this out but got a different answer than the book )anyway here it is.
Q = -T*V*(Volume Expansivity)*(P_f-P_i)
Q = -(298K)*(5.58X10^-5m^3)*(49.5X10^-6K^-1)*(5.056X10^8Pa)
Where i found Volume From Mass/density
and changed Pressure from atm to Pascals
after pluging in all these numbers my answer is -416 N*m or -416J
the answer the book gives is -139.9J

Can anyone see the problem here?
sorry if there is any confusion with symbols this is my first post and do not know how to use the code yet.
Thanks
 
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  • #2
"Isothermal process." Ask yourself what is happening in an "isothermal process."
 
  • #3
Ok I asked my self and I replied the temperature is holding at 298K. What r u getting at? In order for the temp to stay the same heat must leave during compression. Precisely how much is the question being asked.
 
  • #4


Originally posted by rsd_sosu
Now the first part of the question ask how much heat is transferred during the compression?
How much work is done on the copper as it is compressed?
 
  • #5
I talked to my Professor today and he informed me that the answer in the book was indeed incorrect. This is not the first time and probably won't be the last error i find. the text i am using is Heat And Thermodynamics by Zemansky and Dittman which is full of errors in the seventh edition. Anyway thanks for the responses.

The Work involved that you (Doc Al) mentioned was in fact the second of four questions asked. Here it is.

[tex]
W = \int_{P_i}^{P_f} VkP dP = \frac{1}{2} V k P^2_f
[/tex]


[tex]
\frac{1}{2}(5.58X10^{-5}m^3)(6.18X10^-^1^2Pa^{-1})(5.07X10^8Pa)^2
[/tex]


[tex]
= 44.3N-m =44.3J
[/tex]

Just to get a bit more practice with this scrip I will show the Change in internal energy as well, which was the third question.

[tex]
\Delta U = Q + W = -417J + 44.3J = -372.7J
[/tex]

Later,
 
Last edited:

1. How is heat transferred during the compression process?

Heat is transferred during the compression process through various mechanisms such as conduction, convection, and radiation. In conduction, heat is transferred through direct contact between objects. In convection, heat is transferred through the movement of fluids, such as air or water. In radiation, heat is transferred through electromagnetic waves.

2. What factors affect the amount of heat transferred during compression?

The amount of heat transferred during compression is affected by several factors, including the initial temperature and pressure of the system, the type and properties of the materials being compressed, and the rate and duration of the compression process.

3. How does the compression ratio impact the amount of heat transferred?

The compression ratio, which is the ratio of the initial volume to the final volume of a gas, can have a significant impact on the amount of heat transferred during compression. A higher compression ratio means a smaller final volume, resulting in a larger increase in temperature and therefore more heat transferred.

4. Can heat be removed during the compression process?

Yes, heat can be removed during the compression process through various methods such as cooling the compressed gas or using heat exchangers. This is often done in industrial processes to prevent overheating and maintain the desired temperature and pressure levels.

5. How can the amount of heat transferred during compression be calculated?

The amount of heat transferred during the compression process can be calculated using 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. This calculation can be more complex depending on the specific conditions and processes involved.

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