Aboy on the beach holds a spherical balloon filled with air. at 7: 00 am, the temperature on the beach is 35°f and the balloon has a diameter of 20 cm. six hours later, the outside temperature is 100°f. assume that the air is an ideal gas, that the atmospheric pressure remains constant, and that no air was lost or added to the balloon. what is the final diameter of the balloon (in cm)?

The final diameter of the balloon is 20.84 cm.

Explanation:

To answer this problem, because both the number of moles (because no air was lost or added to the balloon) and the pressure remain constant, we can use Charles' law, or the law of volumes:

V₁T₂=V₂T₁

Where V is Volume (in L) and T is temperature (in K). The subscripts 1 and 2 refer to different states of the gas: for this problem, let's say that ₁ refers to the state of the gas at 7:00 am and that ₂ refers to the state 6 hours later.

To calculate the volume occupied by the gas we use the formula for the volume of a sphere:

Thus the volume of the balloon at 7:00 am is 4188.79 cm³

Then we convert °F into K:

Now we use Charles' law to calculate V₂:

V₂=V₁T₂/T₁

V₂=

Lastly we calculate the final diameter of the balloon:

ca has a crystalline lattice with positive ions (since it is a metal, metals are positively charged) and electrons flow freely in its structure since the ca atoms have a large nuclear radius so the electrons are not tightly held, therefore the electrons can flow freely since they are not being highly attracted by the nucleus. moreover, one of the properties of metals are that they are conductors of electricity, thus proving ca is the element.