To solve this problem we will apply the concepts related to the calculation of the surface, volume and error through the differentiation of the formulas given for the calculation of these values in a circle. Our values given at the beginning are


The radius then would be

And

PART A ) For the Surface Area we have that,

Deriving we have that the change in the Area is equivalent to the maximum error, therefore

Maximum error:


The relative error is that between the value of the Area and the maximum error, therefore:


PART B) For the volume we repeat the same process but now with the formula for the calculation of the volume in a sphere, so


Therefore the Maximum Error would be,



Replacing the value for the radius


And the relative Error



I think iron? i’m not 100% sure
Answer:
E_particle = 1,129 10⁻²⁰ J / particle
T= 817.5 K
Explanation:
Energy is a scalar quantity so it is additive, let's look for the total energy of each gas
Gas a
E_a = 2 5000 = 10000 J
Gas b
E_b = 3 8000 = 24000 J
When the total system energy is mixed it is
E_total = E_a + E_b
E_total = 10000 + 24000 = 34000
The total mass is
M = m_a + m_b
M = 2 +3 = 5
The average energy among the entire mass is
E_averge = E_total / M
E_averago = 34000/5
E_average = 6800 J
One mole of matter has Avogadro's number of atoms 6,022 10²³ particles
Therefore, each particle has an energy of
E_particle = E_averag / 6.022 10²³ = 6800 /6.022 10²³
E_particle = 1,129 10⁻²⁰ J / particle
For find the temperature let's use equation
E = kT
T = E / k
T = 1,129 10⁻²⁰ / 1,381 10⁻²³
T = 8.175 102 K
T= 817.5 K
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