Question

1.6. When the ice point $i$ and the steam point $s$ were chosen as fixed points with 100 degrees between them in the original Celsius scale, the ideal-gas temperature of the ice point was written \\ $\theta_i = \frac{100}{r_s - 1}$, \\ where $r_s = \lim (P_s/P_i)$ at constant $V$. \\ (a) Show that the fractional error in $T_i$ produced by an error in $r_s$ is very nearly 3.73 times the fractional error in $r_s$, or \\ $\frac{dT_i}{T_i} = 3.73 \frac{dr_s}{r_s}$, \\ (b) Any ideal-gas temperature may be written \\ $T = T_i r$, \\ where $r = \lim (P/P_i)$ at constant $V$. Show that the fractional error in $T$ is \\ $\frac{dT}{T} = \frac{dr}{r} + 3.73 \frac{dr_s}{r_s}$, \\ (c) Now that the single fixed point of the ideal-gas temperature is a universal constant, show that the fractional error in $T$ is \\ $\frac{dT}{T} = \frac{dr}{r}$, \\ where $r = \lim (P/P_{TP})$ at constant $V$.

          1.6. When the ice point $i$ and the steam point $s$ were chosen as fixed points with 100 degrees between them in the original Celsius scale, the ideal-gas temperature of the ice point was written \\
$\theta_i = \frac{100}{r_s - 1}$, \\
where $r_s = \lim (P_s/P_i)$ at constant $V$. \\
(a) Show that the fractional error in $T_i$ produced by an error in $r_s$ is very nearly 3.73 times the fractional error in $r_s$, or \\
$\frac{dT_i}{T_i} = 3.73 \frac{dr_s}{r_s}$, \\
(b) Any ideal-gas temperature may be written \\
$T = T_i r$, \\
where $r = \lim (P/P_i)$ at constant $V$. Show that the fractional error in $T$ is \\
$\frac{dT}{T} = \frac{dr}{r} + 3.73 \frac{dr_s}{r_s}$, \\
(c) Now that the single fixed point of the ideal-gas temperature is a universal constant, show that the fractional error in $T$ is \\
$\frac{dT}{T} = \frac{dr}{r}$, \\
where $r = \lim (P/P_{TP})$ at constant $V$.

$1.6. When the ice point i and the steam point s were chosen as fixed points with 100 degrees between them in the original Celsius scale, the ideal-gas temperature of the ice point was written = (100)/(rs - 1), where rs = lim (Ps/Pi) at constant V. (a) Show that the fractional error in Ti produced by an error in rs is very nearly 3.73 times the fractional error in rs, or (dTi)/(Ti) = 3.73 (drs)/(rs), (b) Any ideal-gas temperature may be written T = Ti r, where r = lim (P/Pi) at constant V. Show that the fractional error in T is (dT)/(T) = (dr)/(r) + 3.73 (drs)/(rs), (c) Now that the single fixed point of the ideal-gas temperature is a universal constant, show that the fractional error in T is (dT)/(T) = (dr)/(r), where r = lim (P/PTP) at constant V.$

Added by Gary R.

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