Question

A constant-volume gas thermometer is calibrated in dry ice (that is, evaporating carbon dioxide in the solid state, with a temperature of −80.0°C) and in boiling ethyl alcohol (78.0°C). The two pressures are 0.900 atm and 1.635 atm, respectively. What Celsius value of absolute zero does the calibration yield?

Answer 1

To solve this problem, the gas law equation is used in the form of P/T = constant. With the given values and using the Ideal Gas Law, absolute zero in terms of the Celsius scale can be calculated by equating the constants K1 and K2.

Step-by-step explanation:

This problem can be solved by using the gas law equation as the gas is in a constant-volume thermometer. You can write the equation in the form of P/T = constant. This means the ratio of the pressure and the temperature (on an absolute scale) is a constant for each particular gas, in this case, boiling ethyl alcohol and vaporizing carbon dioxide.

You have two points on the PT graph: P1 = 0.900 atm at T1 = -80°C = 193.15 K and P2 = 1.635 atm at T2 = 78°C = 351.15 K. Therefore, the constants K1 = P1/T1 and K2 = P2/T2 based on the Ideal Gas Law.

By equating K1 and K2, we will get absolute zero in terms of Celsius scale. Note that absolute zero is defined as the temperature where gas pressure would theoretically become zero.

Learn more about Gas Law Equation