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Chapter 1: Problem 34

At \(4^{\circ} \mathrm{C}\) a mixture of automobile antifreeze \((50 \%\) water and \(50 \%\) ethylene glycol by volume ) has a density of \(1064 \mathrm{kg} / \mathrm{m}^{3}\). If the water density is \(1000 \mathrm{kg} / \mathrm{m}^{3}\), find the density of the ethylene glycol.

Short Answer

Expert verified
The density of ethylene glycol in the given mixture is \(1128 kg/m³\)

Step by step solution

01

Identifying the given values

Identifying the given values in the exercise: \n\n The density of the mixture, \( \rho_{mix}\) = 1064 kg/m³ \n The density of water, \( \rho_{H2O}\) = 1000 kg/m³ \n The percentage of water and ethylene glycol by volume in the mix = 50 % each. When considering mass, we can thus also presume an equal division as 1:1 or a 50:50 mix by mass, since the problem does not specify the contrary.
02

Formulating the equation to solve for the unknown density

The density of a 50:50 mixture of water and ethylene glycol can be represented as: \(\rho_{mix} = \frac{\rho_{H2O} + \rho_{EG}}{2}\), where \( \rho_{EG}\) is the density of ethylene glycol, the value that we want to find.
03

Solving for the unknown density

Rearrange equation from Step 2 to solve for \( \rho_{EG}\): \(\rho_{EG} = 2\rho_{mix} - \rho_{H2O}\)
04

Substitute the given values into the equation

Substitute the given values into the equation to find the density of ethylene glycol: \(\rho_{EG} = 2*1064kg/m³ - 1000kg/m³ \)
05

Simplify and find the result

On simplifying, we find the density of the ethylene glycol to be 1128 kg/m³.

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Most popular questions from this chapter

One type of capillary-tube viscometer is shown in Video V1.5 and in Fig. P1.57. For this device the liquid to be tested is drawn into the tube to a level above the top etched line. The time is then obtained for the liquid to drain to the bottom etched line.The kinematic viscosity, \(\nu,\) in \(\mathrm{m}^{2} / \mathrm{s}\) is then obtained from the equation \(\nu=K R^{4} t\) where \(K\) is a constant, \(R\) is the radius cf the capillary tube in \(\mathrm{mm}\), and \(t\) is the drain time in seconds. When glycerin at \(20^{\circ} \mathrm{C}\) is used as a calibration fluid in a particular viscometer, the drain time is 1430 s. When a liquid having a density of \(970 \mathrm{kg} / \mathrm{m}^{3}\) is tested in the same viscometer the drain time is 900 s. What is the dynamic viscosity of this liquid?

The viscosity of a certain fluid is \(5 \times 10^{-4}\) pcise. Determine its viscosity in both SI and BG units.

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When a 2 -mm-diameter tube is inserted into a liquid in an open tank, the liquid is observed to rise \(10 \mathrm{mm}\) above the free surface of the liquid (see Video \(V 1.10\) ). The contact angle between the liquid and the tube is zero, and the specific weight of the liquid is \(1.2 \times 10^{4} \mathrm{N} / \mathrm{m}^{3}\). Determine the value of the surface tension for this liquid.
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