Answer to Question #204575 in Molecular Physics | Thermodynamics for Fhulufhedzani

Question

1. On the Rankine temperature scale, which is sometimes used in engineering applications, the ice point is at 491.67 °R and the stem point is at 671.67 °R.

a.) Determine the relationship between the Rankine and Fahrenheit temperature scales.

b.) A healthy person has an oral temperature of 98.67 °F. Calculate what would this reading be on the Rankine temperature scale.

2. Two identical thermometers made of Pyrex glass contain, respectively, identical volumes of mercury and methyl alcohol. If the expansion of the glass is taken into account, calculate how many times greater is the distance between the degree marks of the methyl alcohol thermometer than the distance on the mercury thermometer.

Answer 1

answer:-

1)

(a) We know that on the Fahrenheit scale the freezing point of water is 32 F and boiling point of water is 212 F. The difference between temperatures is $212-32 = 180F.$ The difference between analogous temperatures on the Rankine scale is

$671.67-491.67 = 180 R.$ Therefore 1°R = 1°F. So we should take into account only the difference between the initial points of scales.

0°F = 491.67 -32 =459.67°R. Therefore, t(°F) = t(°R) - 459.67 and t(°R) = t(°F) + 459.67.

(b) If a person has temperature 98.6°F, then on the Rankine scale his temperature will be

t(°R) = t(°F) + 459.67 = 98.6 + 459.67 = 558.27°R

(2)

$\frac{h_a}{h_m}=\frac{\beta _a -\beta_g}{\beta_m-\beta_g}$ ......(formula)

where $\beta_a$ is coefficient of volume expansion of alcohol $=1200\times10^{-6}1/k$

$\beta_g$ is coefficient of volume expansion of glass $=9.9\times10^{-6}1/k$

and $\beta _m$ is coefficient of volume expansion of mercury $= 182\times 10^{-6}1/k$

putting these values in the formula , we get

$\frac{h_a}{h_m}=\frac{1200\times10^{-6}1/k-9.9\times10^{-6}1/k}{182\times 10^{-6}1/k-9.9\times10^{-6}1/k}$

$\boxed{\frac{h_a}{h_m}=6.915}$