[Thermodynamics] Relative fractional error, Ideal-gas-scale, Celsius scale

In summary, the conversation discusses attempts to derive θ in respect to r and θ_i in respect to r_s, with the goal of finding the fractional error. However, the equations used do not match those shown in the given picture and the result does not match the expected value.
  • #1
Je m'appelle
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Homework Statement



http://j.imagehost.org/0069/thermo.jpg [Broken]

Homework Equations


The Attempt at a Solution



OK, so I tried to derive θ in respect to r as in θ(r):

[tex]\frac{d\theta}{dr} = \frac{-100}{(r - 1)^2}[/tex]

Then, I multiplied both sides of the equation by 'dr',

[tex]d\theta = \frac{-100}{(r - 1)^2}dr[/tex]

Then I divided both sides of the equation by θ in order to find the fractional error but it doesn't match with the equation on the picture:

[tex]\frac{d\theta}{\theta} = \frac{dr}{(1 - r)}[/tex]I'm lost.

Anyone?
 
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  • #2
I assume θ_i = T_i? Or is there a difference?

Is θ_i in Celsius and T_i in Kelvin?

So I tried to derive θ_i in respect to r_s as in θ_i(r_s):

[tex]\frac{d\theta_i}{dr_s} = \frac{-100}{(r_s - 1)^2}[/tex]

Then, I multiplied both sides of the equation by 'dr_s',

[tex]d\theta_i = \frac{-100}{(r_s - 1)^2}dr_s[/tex]

Then I divided both sides of the equation by θ in order to find the fractional error but it doesn't match with the equation on the picture:

[tex]\frac{d\theta_i}{\theta_i} = \frac{dr_s}{(1 - r_s)}[/tex]But the result should be something like:

[tex]\frac{d\theta_i}{\theta_i} = 3,73\frac{dr_s}{r_s}[/tex]
 
Last edited:
  • #3
sorry, ignore this post.
 

1. What is relative fractional error in thermodynamics?

Relative fractional error is a measure of the accuracy of a measurement in relation to the true value. It is calculated by taking the difference between the measured value and the true value, dividing it by the true value, and multiplying by 100%. It is commonly used in thermodynamics to assess the precision of temperature measurements.

2. How is the Ideal-gas-scale related to thermodynamics?

The Ideal-gas-scale is a temperature scale that is based on the properties of an ideal gas at constant pressure. It is directly related to thermodynamics because temperature is a fundamental property in this field and the Ideal-gas-scale is one of the ways to measure it.

3. What is the significance of the Celsius scale in thermodynamics?

The Celsius scale is a commonly used temperature scale in thermodynamics. It is based on the freezing and boiling points of water, with 0 degrees representing the freezing point and 100 degrees representing the boiling point. It is used in many thermodynamic calculations and is the standard unit for measuring temperature in most countries.

4. How does relative fractional error impact thermodynamic calculations?

Relative fractional error can significantly impact the accuracy of thermodynamic calculations. It is important to keep this error as low as possible to ensure the reliability of the results. This is especially crucial in industries where precise temperature measurements are crucial for safety and efficiency, such as in the production of pharmaceuticals or petrochemicals.

5. Can relative fractional error be eliminated completely in thermodynamics?

No, it is impossible to completely eliminate relative fractional error in any measurement, including in thermodynamics. However, it can be minimized by using precise and calibrated instruments, performing multiple measurements, and using statistical analysis to determine the most accurate value. It is also important to consider the limitations of the equipment and the environment in which the measurement is taking place.

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