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Travka [436]
4 years ago
9

Two soils are fully saturated with liquid (no gas present) and the soils have the same void ratio. One soil is saturated with wa

ter and the other is saturated with alcohol. The unit weight of water is approximately 1g/cm3 while that of alcohol is about 0.8 g/cm3. Which soil sample has the larger water content? Why?
Engineering
1 answer:
mariarad [96]4 years ago
5 0

Answer:

water sample have more water content

Explanation:

given data

soil 1 is saturated with  water

unit weight of water = 1 g/cm³

soil 2 is saturated with alcohol

unit weight of alcohol  = 0.8 g/cm³

solution

we get here water content that is express as

water content = S_s \times \gamma _w   ....................1

here soil is full saturated so S_s is 100% in both case

so put here value for water

water content = 100 % ×  1

water content = 1 g

and

now we get for alcohol that is

water content  = 100 % × 0.8

water content  = 0.8 g

so here water sample have more water content

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Final volume of steam = 5 × V₁

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\dfrac{p_1}{p_2} = \left (\dfrac{V_2}{V_1} \right )^k = \left [\dfrac{T_1}{T_2}   \right ]^{\dfrac{k}{k-1}}

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We therefore have;

\dfrac{1060}{p_2} = \left (\dfrac{5\cdot V_1}{V_1} \right )^{1.33}

P_2= \dfrac{1060}{5^{1.33}}  = 124.65 \ kPa

\left [\dfrac{V_2}{V_1} \right ]^k = \left [\dfrac{T_1}{T_2}   \right ]^{\dfrac{k}{k-1}}

\left [\dfrac{V_2}{V_1} \right ]^{k-1} = \left \dfrac{T_1}{T_2}   \right

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T₁ = 1.70083·T₂

T₂ - T₁ = T₂ - 1.70083·T₂

Whereby the temperature of saturation T₁ = 179.866 °C = 453.016 K, we have;

T₂ = 453.016/1.70083 = 266.35 K

ΔU = 3×c_v×(T₂ - T₁)

c_v = cv for steam at 453.016 K = 1.926 + (453.016 -450)/(500-450)*(1.954-1.926) = 1.93 kJ/(kg·K)

cv for steam at 266.35 K = 1.86  kJ/(kg·K)

We use cv given by  (1.93 + 1.86)/2 = 1.895 kJ/(kg·K)

ΔU = 3×c_v×(T₂ - T₁) = 3*1.895 *(266.35 -453.016) = -1061.2 kJ/kg

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h_g = 2777.12 kJ/kg

V_g = 0.194349 m³/kg

p = 1000 kPa

U_{g1} = 2777.12 - 0.194349 * 1060 = 2571.11 kJ/kg

The final specific internal energy of the system is therefore, U_{g1} + ΔU = 2571.11 - 1061.2 = 1509.91 kJ/kg.

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