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In: Physics

*Please answer all three parts Three Part Question: X. (A) NASA Atmospheric Mission balloons use helium...

*Please answer all three parts

Three Part Question: X. (A) NASA Atmospheric Mission balloons use helium that expands to almost 1 million cubic meter at the top of the atmosphere where pressure is 0.003 atm only. Even though it takes about 2.5 hours to get to this altitude, it is assumed that the rise is fast enough to be considered as adiabatic. Find the initial volume of the helium at the ground level. (Helium is a mono-atomic gas). (B) If the initial temperature of the gas was 15 degree celsius what is the temperature of the gas at the top? Ignore real atmospheric temperature changes. (C) What is the change in internal energy of the gas?

*Please provide steps, explanations, and formulas.

*Explain to me as if I know nothing

*I am genuinly trying to learn and understand. Please and thank you.

Expert Solution

given

V₂ = 1 million cubic meter

= 10¹⁸ m³

P₂ = 0.003 atm

= 1.67 for mono atomic gas

a )

using P V

P₁ V₁ = P₂ V₂

V₁ = ( P₂ V₂ / P₁ )

= ( 0.003 x 10^{18x 1.67} )

the initial volume of the helium at the ground level is V₁ = 3 x 10¹⁶ m/sec

b )

T₁ = 15^oC

= 288 K

T V^-1 = constant

T₁ V₁^-1 = T₂ V₂^-1

T₂ = T₁ ( V₁ / V₂ )^-1

= 288 x ( 3 x 10¹⁶ / 10¹⁸ )^1.67-1

the temperature of the gas at the top is T₂ = 27.4 K

or

T₂ = 27.4 - 273

the temperature of the gas at the top is T₂ = - 245.5^oC

c )

dU = dQ - dW

dQ = 0 for adiabatic process

dU = dW

= ( P₁ V₁ - P₂ V₂ ) / - 1

= R ( T₁ - T₂ ) / ( - 1)

= 8.314 x 260.6 / 1.67 - 1

the change in internal energy of the gas is dU = - 3233.77 J

genius_generous answered 1 hour ago

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