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### An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

# The Rankine temperature scale(abbreviated $°R$) uses the same scale size degrees as Fahrenheit, but measured up from absolute zero like Kelvin(so Rankine is to Fahrenheit as Kelvin is to Celsius). Find the conversion formula between Rankine and Fahrenheit and also between Rankine and Kelvin. What is the room temperature on the Rankine scale?

R = $\frac{9}{5}K$ and R = 536.67$°R$

See the step by step solution

## Step 1: Writing the conversion equations of Kelvin to Celsius and Rankine to Fahrenheit.

The conversion equation for Kelvin to Celsius is,

K = C + 273.15 -----------(1)

and similarly conversion equation for Rankine to Fahrenheit is,

R = F + 459.67 -----------(2)

## Step 2: Comparison of Kelvin and Rankine scales at absolute zero,

But we know that, F = $\frac{9}{5}C+32$

substituting this in equation (2),

R = $\frac{9}{5}C+491.67$

substituting C from equation (1), we get,

R = $\frac{9}{5}K$

## Step 3: Standard room temperature in Celsius scale usually refers to 25°C and using the conversion formula to write in Rankine scale.

The room temperature in Kelvin scale will be 25 + 273.15 = 298.15K

Applying the conversion formula of Kelvin to Rankine scale, we get,

R = $\frac{9}{5}\left(298.15\right)$

R = 536.67$°R$