In this experiment a student found that when she increased the temperature of
a \(550 \mathrm{mL}\) sample of air from \(22.3^{\circ} \mathrm{C}\) to
\(29.7^{\circ} \mathrm{C},\) the pressure of the air went from \(1009 \mathrm{cm}
\mathrm{H}_{2} \mathrm{O}\) up to \(1033 \mathrm{cm} \mathrm{H}_{2} \mathrm{O}\).
Since the air expands linearly with temperature, the equation relating \(P\) to
\(t\) is of the form:
$$P=m t+b$$
a. What is the slope of the line? (Find the change in \(P\) divided by the
change in \(t\).) \(m=\)_____ \(\mathrm{cm} \mathrm{H}_{2} \mathrm{O} /^{\circ}
\mathrm{C}\)
b. Find the value of \(b .\) (Substitute known values of \(P\) and \(t\) into
Equation 9 and solve for \(b\).)\(b=\)_____
c. Express Equation 9 in terms of the values of \(m\) and \(b\). \(P=\)
d. At what temperature \(t\) will \(P\) become zero? \(P=0 \quad\) at \(\quad
t=\)_____ \(^{\circ} \mathrm{C}=t_{\mathrm{o}}=-A\)
e. The temperature in Part d is the absolute zero of temperature. Lord Kelvin
suggested that we set up a scale on which that temperature is 0 K. On that
scale, \(T=t+A\). Show that, on the Kelvin scale, your equation reduces to \(P=m
T\).
