In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is 1.16×10^8 Pa (about 1.15×10^3 atm). (a) If a cubic meter of water is taken from the surface to this depth, what is the change in its volume? (Normal atmospheric pressure is about 1.0×10^5 Pa. Assume that k for seawater is the same as the freshwater value given in Table 11.2.)

Video transcript

Welcome back everybody. We have an ice cube that is traveling up to the peak of mount Everest. Now we're told at the top of the atmospheric pressure is 0.31 80 M. At the sea level. It is simply 1 80 M. And although the cube will not melt, there is going to be a change in volume. And we need to figure out what that is. Given that the compressibility constant of an ice cube is five times 10 to the negative 10th. That's close to the -1. Well, I'm looking at all these values here and I'm gonna use this equation. We know that the bulk model lists which I'm just gonna give by be here right is equal to negative change in pressure over our desired change in volume divided by the initial volume. The bulk module list is simply just one over the compressibility constant. So rearranging you know these these equations here you can get that are desired. Change in volume is given by the negative of the change in pressure over one over K times our initial volume. Before plugging in these terms. Since our compressibility constant is in pascal's we need to make sure that our change in pressure is in pascal's as well. So our change in pressure is given by 1 80 M minus 800.31 80 M is equal to zero per 0. 80 M. In 1 80 M. There is 1.13 times 10 to the fifth pascal's giving us that our change in pressure is 6. times 10 to the fourth pascal's. With that in mind. Let's go ahead and plug that into the above equation. We have that. This is negative 6.99 times 10 to the fourth over one, divided by five times 10 to the negative 10th times our original volume, which was just one m cubed. This gives us our final answer that are changing volume is negative 3.5 times 10 to the negative fifth meters cubed, corresponding to our answer. Choice of a Thank you all so much for watching. Hope this video helped. We will see you all in the next one.