Question

A gas follows pV=bp+cT on an isothermal curve, where p is the pressure, V is the volume, b is a constant, and c is a function of temperature. If c can be determined from the measurement of a single other thermodynamic parameter, it establishes a temperature scale for this gas. Show that a temperature scale under an isochoric process can be established with this gas, with pressure being the measured parameter, and is identical to that of an ideal gas.

Answer 1

Under an isochoric process, a temperature scale can be established with a gas that follows the equation pV=bp+cT. This temperature scale is identical to that of an ideal gas.

Step-by-step explanation:

An isochoric process refers to a process in which the volume of a gas remains constant. In this case, if we use pressure as the measured parameter, we can establish a temperature scale for this gas. By rearranging the equation pV = bp + cT and substituting V=constant, we get p = b + cT/V. Since V is constant, we can treat it as a constant and rewrite the equation as p = b + (c/V)T.

This equation is identical to that of an ideal gas equation, which is p = RT/V, where R is the gas constant. By comparing the two equations, we can see that b is equivalent to RT/V and (c/V) is equivalent to R. Therefore, the temperature scale established under an isochoric process with this gas is identical to that of an ideal gas.