Answer to Question #230222 in Molecular Physics | Thermodynamics for sphume

Question

A mercury thermometer is at an initial temperature of 24 C and it is placed in a glass of water at 8 C. The thermometer has a spherical reservoir of diameter D = 1.4 cm3 , and a column of diameter d = 1.00 mm. At 4 C the mercury fills the reservoir but does not enter the column. The linear expansion coefficient of mercury  = 6.00 × 104 K1 . The mercury column has initial height hi and it decreases to a final height hf = hi/2 during the process of arriving at equilibrium with the water. (a) Explain why the process is not a quasi-equilibrium process. (3) (b) Calculate the temperature of the water.

Answer 1

(a) The process has to undergo several processes that are done slowly enough for the system to remain at thermodynamic equilibrium at each instant. Since this does not occur and because we are unable to model the path for this process is the reason why there is no quasi-equilibrium process: the thermometer would have to change temperature very slowly until it reaches thermal equilibrium with the water at 8°C, since the change in height for the mercury column is not proportional to that we have to consider the thermal equilibrium has not been reached yet, thus remarking this is not a quasi-equilibrium process.

(b) Since $\Delta h=h_f-h_i=-h_i/2$, we have to consider that the change in temperature has to be half of the change in temperature needed for the column to reach the height $h_i$. Since $\Delta T = (24-(-4))°C=28 \,°C$ , the new change in temperature would be: $\Delta T'=\Delta T / 2 = 14\, °C$. Since the initial temperature is -4 °C, the temperature of the thermometer will be $T_f'=-4\,°C+14\,°C=10\,°C$.

In conclusion, the temperature of the thermometer is 10 °C.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.