A glass tube has one end in a dish of mercury and the other end closed by a stopcock. The distance from the surface of the mercury to the bottom of the stopcock is 850 mm. The apparatus is at 25 °C, and the mercury level in the tube is the same as that in the dish.

(a) Show on drawing (1) what the approximate level of mercury in the tube will be when the temperature of the entire apparatus is lowered from +25 °C to -25 °C.

Video transcript

Welcome back everyone. We're told that in an experiment one of the open ends of a glass tube is in a dish filled with mercury while the other end is closed by a stop cock. The distance between the surface of mercury to the stop cock is at 20°C. The height of mercury in the tube is equal to the height of mercury in the dish, Which image corresponds to the level of mercury in the tube when the temperature is lowered to negative 50°C. So we need to consider the four options below. And we want to recall our formula for gay loose ax, loss of pressure related to temperature, where our initial pressure divided by our initial temperature is related to our final pressure divided by our final temperature. And sorry, this is a two here. Now from the prompt, it states that the height of mercury in the tube is equal to the height of mercury in the dish, meaning that our initial pressure should equal our atmospheric pressure. And we also know that because the prompt states set this tube which records our level of mercury is closed with a stop cock. So it should be related to the external pressure being our pressure of our atmosphere. And we want to recall that atmospheric pressure is always of mercury. So now we want to recognize our other terms from the prompt. We're told our initial temperature as 20°C. Now for our formula, we want this to be in Kelvin. So we're going to add to 73.15 Kelvin or just to 73.15 to get our Kelvin temperature of 2 93.15 Kelvin. And so for our final temperature were also given that in the prompt as negative 50°C. And we're going to convert this to Kelvin by adding to 73.15. This is going to give us a final temperature of 223. Kelvin. Now that we have these values, we want to recall that since our other end of our tube is closed with a stop cock, we can make the relation that our pressure of the atmosphere or we can say external pressure, which we already know is 760 millimeters of mercury for the atmosphere is equal to the pressure of our tube plus the pressure of the mercury exerted against the tube. And so we're going to isolate this so that we can say our pressure of mercury is equal to the difference between our atmospheric pressure millimeters of mercury minus the pressure of our tube. Once the temperature decreases to 50 negative 50 degrees Celsius. And that is why we need to solve for P two first before we can find the pressure of mercury. So we're going to find P two where we would say that our final pressure is equal to the initial pressure multiplied by the Final temperature divided by the initial temperature. So plugging in our values that we know, we know that our initial pressure as we stated, is our atmospheric pressure of 760 of mercury. We're multiplying this by our final temperature which we converted to 200 23. And sorry about that, we converted it to 223 Kelvin. We're just going to simplify it and leave off that .15 unit. And then we are going to divide by our initial temperature which we converted to 293 Kelvin. And so this tells us that once our temperature decreases to negative 50°C, we have a final pressure of 578 mm of mercury. And this is the final pressure of our tube. So now that we have this value, we're going to go ahead and find our final pressure of our mercury. Exerted by the final pressure of the mercury that is being exerted onto the tube equal to again the difference between 760 millimeters of mercury for our atmosphere subtracted from the pressure of the tube. Once the temperature decreases to negative 50 degrees Celsius, which we just found to be 578 millimeters of mercury. This difference yields a pressure of mercury which should be equal to 182 millimeters of mercury, meaning that when we go back to our answer choices, we want to find which answer choice corresponds to the level of 182 millimeters of mercury, and we can see that that best corresponds to, We would say, choice B looks about to be 182 mm of mercury, according to our measure of the tube. And so we would confirm that choice B would be our final answer. To complete this example. I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.