Final answer:
According to Gay-Lussac's Law, the temperature of a gas is directly proportional to its pressure when volume is held constant. Therefore, the temperature when the pressure is 10 cm Hg is one-tenth of the initial temperature.
Step-by-step explanation:
According to Gay-Lussac's Law, the pressure of a gas is directly proportional to its temperature when volume is held constant. This relationship can be expressed as:
P1/T1 = P2/T2
Where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
In this case, the gas is initially at 100 cm Hg at the melting ice temperature. Let's call this condition A. When the pressure decreases to 10 cm Hg, let's call this condition B.
Using the equation above, we can set up the following ratio:
100/T1 = 10/T2
Cross multiplying, we get:
100T2 = 10T1
Dividing both sides by 10, we get:
10T2 = T1
So, the temperature T2 when the pressure is 10 cm Hg is one-tenth the temperature T1 when the pressure is 100 cm Hg.
Therefore, the temperature when the pressure is 10 cm Hg is one-tenth of the initial temperature.