Answer:
Explanation:
The gas ideal law is
PV= nRT (equation 1)
Where:
P = pressure
R = gas constant
T = temperature
n= moles of substance
V = volume
Working with equation 1 we can get

The number of moles is mass (m) / molecular weight (mw). Replacing this value in the equation we get.
or
(equation 2)
The cylindrical container has a constant pressure p
The volume is the volume of a cylinder this is

Where:
r = radius
h = height
(pi) = number pi (3.1415)
This cylinder has a radius, r and height, h so the volume is 
Since the temperatures has linear distribution, we can say that the temperature in the cylinder is the average between the temperature in the top and in the bottom of the cylinder. This is:
Replacing these values in the equation 2 we get:
(equation 2)
The half life of uranium- 238 is
4.46 x10^9 years
Explanation
Half life is the time taken for the radioactivity of a isotope to fall to half its original value.
The original mass of uranium-238 is 4.0 mg
Half of original mass of uranium = 4.0 mg /2 = 2.0 mg
since it take 4.46 x 10^ 9 years for the sample to half the half life of uranium -238 = 4.46 x10^9 years
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