Physics

Problem

A student records pairs of values of the speed of sound

v

and the absolute temperature

T

of air and plots

v

against

\sqrt{T}

. The plotted points lie close to a straight line. a. (i) Explain qualitatively why a graph of

v

versus

\sqrt{T}

for a given gas is expected to be a straight line. b. (ii) State what physical constant(s), if any, can be extracted from the gradient of such a line and justify your answer. c. (iii) Two of the data points are

(T=273\,\text{K},\,v=331\,\text{m\,s}^{-1})

and

(T=313\,\text{K},\,v=355\,\text{m\,s}^{-1})

. Using only these two points, estimate the numerical value of the gradient

\dfrac{dv}{d\sqrt{T}}

and interpret its physical meaning.

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