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uc22912
12.02.2020 •
Mathematics
Two containers, X and Y, are each filled by an ideal gas at the same temperature. The volume of Y is half the volume of X. The number of moles of gas in Y is three times the number of moles of the gas in X. The pressure of the gas in X is PX and the pressure of the gas in Y is PY. What is the ratio LaTeX: \frac{P_X}{P_Y}P Y P Y
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Ответ:
The answer to the question is
The ratio of the two gas pressures
, that is Px to Py = 1/6
Step-by-step explanation:
Let the gases Volumes be V₁ and V₂
Where volume of X = V₁ and
volume of Y = V₂
The volume of Y is half the volume of X
∴ V₂ =
× V₁
Let the number of moles be n₁ and n₂ in X and Y respectively
therefore n₂ = 3 × n₁
The pressure of the gas in X is Pₓ and the pressure of the gas in Y is
then we have
P₁ × V₁ = n₁ × R × T₁ , and P₂ × V₂ = n₂ × R × T₂
(P₁ × V₁)/(n₁ × T₁) = (P₂ × V₂)/(n₂ × T₂)
but T₁ = T₂
Therefore
(P₁ × V₁)/n₁ = (P₂ × V₂)/n₂. However n₂ = 3 × n₁ and V₂ =
× V₁ therefore substituting in the equation we have
(P₁ × V₁)/n₁ = (P₂ ×
× V₁ )/(3 × n₁) from where
P₁ /P₂ = (
× V₁ × n₁)/(V₁×3 × n₁) =0.5/3 = 1/6
The ratio of
= 1/6
Ответ:
Let x be the mysterious number. So...
2x + 3 = 20
Subtract both sides by 3:
2x = 17
Divide both sides by 2:
x = 17/2