Thermodynamics dimensional analysis- off by 10

In summary, the problem involves using the ideal gas equation to solve for specific volume with given values for pressure and temperature. The attempt at a solution includes solving for the gas constant and then plugging in values to solve for specific volume. However, there was an error in converting the given molar mass to kg/kmol, which resulted in an incorrect final answer. After realizing the mistake, the correct answer was found.
  • #1
darthxepher
56
0

Homework Statement


I am going crazy! The problem tells me to use the ideal gas equation to solve for the specific volume. They give the pressure, 15 MPa, and the temperature, 623 K. However, solving it is not the problem. The problem is that I keep on getting the answer off by a factor of 10^3!



Homework Equations


P = Pressure
v = specific volume
R = gas constant
T = temperature

Pv = RT
v = RT/P

The Attempt at a Solution



1. Solve for gas constant

M (molecular mass) = 0.01802 kg/kmol
R (universal) = 8.314 (kPa*m^3)/(kmol*K)

R = ((8.314 kPa*m^3)/ 1 kmol*K) * (1 kmol/.01802 kg)
R = 461.4 (kPa*m^3)/(K*kg)

2. Solve for Specific volume

v = (461.4 (kPa*m^3)/(K*kg))*(623K)/((15*10^3) kPa)

v = 19.16 (m^3)/kg

But the answer should be 0.0191 instead of 19.16...
 
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  • #2
Which substance has the molar mass of 0.01802 kg/kmol = 0.01802 g/mol? The lightest molar mass (that of H2) is 2 g/mol!

ehild
 
  • #3
THANKS!
I figured out what i did wrong.

18.02 g/mol = 18.02 kg/kmol!

:P
 

1. What is thermodynamics and why is it important?

Thermodynamics is the branch of physics that deals with the relationships between heat, energy, and work. It is important because it helps us understand and predict how energy is transferred and transformed in different systems, from engines to refrigerators.

2. How does dimensional analysis relate to thermodynamics?

Dimensional analysis is a mathematical tool used to analyze and understand physical quantities and their relationships. In thermodynamics, it is used to check the dimensional consistency of equations and to derive new equations by combining different physical quantities.

3. What does it mean to be "off by 10" in thermodynamics?

Being "off by 10" in thermodynamics means that there is a discrepancy of 10 units in a particular measurement or calculation. This could be due to human error, experimental limitations, or simplifications made in theoretical models.

4. How can dimensional analysis help with solving thermodynamics problems?

Dimensional analysis can help with solving thermodynamics problems by providing a systematic approach to analyze the relationships between different physical quantities. It can also be used to check the accuracy of calculations and to identify any missing variables in equations.

5. What are some real-life applications of thermodynamics and dimensional analysis?

Thermodynamics and dimensional analysis have numerous applications in our daily lives, from cooking and heating our homes to designing and improving energy-efficient technologies. They are also essential in fields such as engineering, meteorology, and environmental science.

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