Answer:
The initial volume of the system: <u>V₁ = 53.06 L</u>
Explanation:
Given: heat absorbed by system: q = 50.5 J, Pressure: P = 0.491 atm, Final volume: V₂ = 56.2 L, The change in the internal energy: ΔE = -106.0 J
Initial volume: V₁ = ? L
<u>According to the First Law of Thermodynamics</u>:
ΔE = q - PΔV
⇒ PΔV = q - ΔE = 50.5 J - (-106.0 J) = 156.5 J
As, 1 L∙atm = 101.3 J ⇒ 1 J = (1 ÷ 101.3) L∙atm
⇒ PΔV = 156.5 J = (156.5 ÷ 101.3) L∙atm = 1.54 L∙atm
So,
ΔV = 1.54 L∙atm ÷ P = 1.54 L∙atm ÷ 0.491 atm = 3.14 L
∵ ΔV = V₂ - V₁ = 3.14 L
⇒ V₁ = V₂ - 3.14 L = 56.2 L - 3.14 L = <u>53.06 L</u>
<u>Therefore, the initial volume of the system: V₁ = 53.06 L</u>
This the reason and how it works
Answer:
P₂ ≅ 100 atm (1 sig. fig. based on the given value of P₁ = 90 atm)
Explanation:
Given:
P₁ = 90 atm P₂ = ?
V₁ = 18 Liters(L) L₂ = 12 Liters(L)
=> decrease volume => increase pressure
=> volume ratio that will increase 90 atm is (18L/12L)
T₁ = 272 Kelvin(K) T₂ = 274 Kelvin(K)
=> increase temperature => increase pressure
=> temperature ratio that will increase 90 atm is (274K/272K)
n₁ = moles = constant n₂ = n₁ = constant
P₂ = 90 atm x (18L/12L) x (274K/272K) = 135.9926471 atm (calculator)
By rule of sig. figs., the final answer should be rounded to an accuracy equal to the 'measured' data value having the least number of sig. figs. This means P₂ ≅ 100 atm based on the given value of P₁ = 90 atm.