- #1

Undoubtedly0

- 98

- 0

Hi all. I have ran into a problem in converting from imperial to SI units, as follows.

The ideal gas constant for air is often given in imperial units as

[tex]R = 1716 \frac{ft*lbf}{slug*°R} [/tex]

where

[tex] 1 ft*lbf = 1.356(10^{-3}) kJ [/tex]

[tex] 1 slug = 14.59 kg [/tex]

[tex] °R = \frac{9}{5}K [/tex]

Thus making these substitutions gives

[tex]R = 1716 \frac{ft*lbf}{slug*°R} = 1716 \frac{(1.356(10^{-3}) kJ)}{(14.59 kg)(\frac{9}{5}K)} = 0.0886 \frac{kJ}{kg*K}[/tex]

Yet it is quite common knowledge that in reality,

[tex] R = 0.287 \frac{kJ}{kg*K} [/tex]

Somewhere, then, in my conversion, there must be an error. I found that if I instead reversed the temperature conversion to be °R = K*5/9, the desired result is given - but how could this be? Surely it is must be true that °R = K*9/5.

Thanks for the help.

The ideal gas constant for air is often given in imperial units as

[tex]R = 1716 \frac{ft*lbf}{slug*°R} [/tex]

where

[tex] 1 ft*lbf = 1.356(10^{-3}) kJ [/tex]

[tex] 1 slug = 14.59 kg [/tex]

[tex] °R = \frac{9}{5}K [/tex]

Thus making these substitutions gives

[tex]R = 1716 \frac{ft*lbf}{slug*°R} = 1716 \frac{(1.356(10^{-3}) kJ)}{(14.59 kg)(\frac{9}{5}K)} = 0.0886 \frac{kJ}{kg*K}[/tex]

Yet it is quite common knowledge that in reality,

[tex] R = 0.287 \frac{kJ}{kg*K} [/tex]

Somewhere, then, in my conversion, there must be an error. I found that if I instead reversed the temperature conversion to be °R = K*5/9, the desired result is given - but how could this be? Surely it is must be true that °R = K*9/5.

Thanks for the help.

Last edited: