Heat transfer and mercury

In summary, in this conversation, the pressure on 0.01 litres of mercury is increased reversibly and isothermally from zero to 1000 atm at room temperature (293 K). The values of the coefficient of volume expansion and isothermal compressibility for mercury are given. The task is to find the amount of heat transferred, work done, and change in internal energy during this compression, assuming that the volume does not change significantly. The first law of thermodynamics is used to find the final temperature and calculate the work done.
  • #1
Winzer
598
0

Homework Statement


The pressure on 0.01 litres of mercury is increased reversibly and isothermally
from zero to 1000 atm at room temperature (293 K). Mercury has a coefficient
of volume expansion β = 1.82 × 10−4 K−1 , and an isothermal compressibility
κT = 4.02 × 10−11 Pa−1 . Note: 1 atm= 1.013 × 105 Pa. Assuming that the
volume, V , changes very little, find
(i) how much heat is transferred in the compression;
(ii) the work done during the compression;
(iii) the change in internal energy.

Homework Equations


[tex]T dS= C_p dT -\beta V dP [/tex]
[tex] \oint \frac{\def\dbar{{\mathchar'26\mkern-12mu d}Q}
\dbar}{T}=0[/tex]
[tex]\def\dbar{{\mathchar'26\mkern-12mu d}Q}
\dbar=C_v dT[/tex]

The Attempt at a Solution


I am attempting to find the final temp so I can implement: [tex]\def\dbar{{\mathchar'26\mkern-12mu d}Q}
\dbar=C_v dT[/tex]

Since the process is reversible, and under a complete cycle [tex] \oint \frac{\def\dbar{{\mathchar'26\mkern-12mu d}Q} \dbar}{T}=0[/tex] I set [tex]dS=0[/tex]. Getting [tex] C_p \int \frac{dT}{T}=\beta T V \int dP [/tex] Is this correct so far?
 
Physics news on Phys.org
  • #2
Your first and last equations doesn't look right. Check your units and your T's.
 
  • #3
I'd start with the first law.
 

1. What is heat transfer?

Heat transfer is the process of energy transfer from a hotter object or region to a cooler one. This transfer can occur through three mechanisms: conduction, convection, and radiation.

2. How does heat transfer occur through conduction?

In conduction, heat is transferred through a solid or stationary medium, such as a metal rod. The heat energy is transferred through molecular collisions, causing the molecules in the cooler region to gain energy and become hotter.

3. Can heat transfer occur in a vacuum?

Yes, heat transfer can occur in a vacuum through radiation. Radiation is the transfer of heat energy through electromagnetic waves, which do not require a medium to travel through.

4. What is the relationship between heat transfer and mercury?

Mercury is a good conductor of heat, meaning it allows heat to transfer through it easily. In fact, mercury is often used in thermometers because it expands and rises when heated, making it a good indicator of temperature changes.

5. How is heat transfer measured in relation to mercury?

Heat transfer in relation to mercury can be measured using a thermometer. The temperature change of the mercury inside the thermometer indicates the amount of heat transferred to or from the object being measured.

Similar threads

  • Advanced Physics Homework Help
Replies
2
Views
894
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
16
Views
3K
Replies
1
Views
497
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Thermodynamics
Replies
2
Views
721
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
839
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
5K
Back
Top