A fluid having a thermal coefficient of volume expansion γ is filled in a cylindrical vessel up to a height h0 . The coefficient of linear thermal expansion of the material of the vessel is α . If the fluid is heated with the vessel, then find the level of liquid when the temperature increases by Δ θ .

Question

A fluid having a thermal coefficient of volume expansion &gamma; is filled in a cylindrical vessel up to a height h0 . The coefficient of linear thermal expansion of the material of the vessel is α . If the fluid is heated with the vessel, then find the level of liquid when the temperature increases by Δ θ . (A) (h0 (. 1 + Î³Îθ .)/(. 1 + 2 Î±Îθ .)) (B) (h0 (. 1 + Î³Îθ .)/(. 1 + 3 Î±Îθ .)) (C) (h0 (. 1 + Î³Îθ .)/(. 1 + Î±Îθ .)) (D) h0(. 1 + γΔθ .)

Tardigrade Admin · Accepted Answer

Abase=A0(1 + Î²Î T)=A0(.1+2Î±Îθ .) Vfluid=V0(1 + Î³Î T)=A0h0(.1+Î³Îθ .) Ah=A0(1 + 2 Î±Îθ )h=A0h0(.1+Î³Îθ .) h=(h0 (. 1 + Î³Îθ .)/(. 1 + 2 Î±Îθ .))

$\frac{h _{0} ( 1 + γ Δ θ )}{( 1 + 2 α Δ θ )}$

$\frac{h _{0} ( 1 + γ Δ θ )}{( 1 + 3 α Δ θ )}$

$\frac{h _{0} ( 1 + γ Δ θ )}{( 1 + α Δ θ )}$

$h_{0} (1 + γ Δ θ)$

$A_{ba se} = A_{0} (1 + β Δ T) = A_{0} (1 + 2 α Δ θ)$
$V_{f l u i d} = V_{0} (1 + γ Δ T) = A_{0} h_{0} (1 + γ Δ θ)$
$A h = A_{0} (1 + 2 α Δ θ) h = A_{0} h_{0} (1 + γ Δ θ)$
$h = \frac{h _{0} ( 1 + γ Δ θ )}{( 1 + 2 α Δ θ )}$

(1+2αΔθ)h0​(1+γΔθ)​

(1+3αΔθ)h0​(1+γΔθ)​

(1+αΔθ)h0​(1+γΔθ)​

h0​(1+γΔθ)

Abase​=A0​(1+βΔT)=A0​(1+2αΔθ) Vfluid​=V0​(1+γΔT)=A0​h0​(1+γΔθ) Ah=A0​(1+2αΔθ)h=A0​h0​(1+γΔθ) h=(1+2αΔθ)h0​(1+γΔθ)​

$\frac{h _{0} ( 1 + γ Δ θ )}{( 1 + 2 α Δ θ )}$

$\frac{h _{0} ( 1 + γ Δ θ )}{( 1 + 3 α Δ θ )}$

$\frac{h _{0} ( 1 + γ Δ θ )}{( 1 + α Δ θ )}$

$h_{0} (1 + γ Δ θ)$

$A_{ba se} = A_{0} (1 + β Δ T) = A_{0} (1 + 2 α Δ θ)$
$V_{f l u i d} = V_{0} (1 + γ Δ T) = A_{0} h_{0} (1 + γ Δ θ)$
$A h = A_{0} (1 + 2 α Δ θ) h = A_{0} h_{0} (1 + γ Δ θ)$
$h = \frac{h _{0} ( 1 + γ Δ θ )}{( 1 + 2 α Δ θ )}$