(8%) Problem 9: Helium is a very important element for both industrial and research applications. In its gas form it can be used

for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 125 moles of Helium gas at room temperature (T = 20° C). The cylinder has a radius of r = 17 cm and a height h = 1.64 m.What pressure is Helium gas under?

Physics

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What is the freezing point of radiator fluid that is 50% antifreeze by mass? k f for water is 1.86 ∘ c/m?

Maru [3345]

Ethylene glycol is known as the main component found in antifreeze.
The molecular formula for ethylene glycol is C₂H₆O₂.
Its molar mass is calculated as C₂H₆O₂ = (2×12) +(6×1) + (216) = 62g/mol
Given that antifreeze comprises 50% by weight, there exists 1 kg of ethylene glycol mixed with 1 kg of water.
ΔTf = Kf×m
ΔTf refers to the change in the freezing point.
= starting temperature of water - freezing temperature of the solution
= 0°C - Tf
= -Tf
Kf stands for the freezing point depression constant of water, which is 1.86°C/m
m is the molarity of the solution.
=(mass/molar mass) where mass of solvent is in kg
=1000g/62 (g/mol) /1kg
=16.13m
Substituting the value into the equation gives us
-Tf = 1.86 × 16.13 = 30
thus Tf = -30°C

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A composite wall separates combustion gases at 2400°C from a liquid coolant at 100°C, with gas and liquid-side convection coeffi

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Response:

$\text{heat loss} = 24864.05 \ W/m^2$

Clarification:

$T_1$ , $T_2$ represent the temperatures of gases and liquids in Kelvins,

$t_1$ and $t_2$ denote the thicknesses of the gas layer and steel slab in meters,
$h_1$ , $h_2$ are the convection coefficients for gas and liquid in $W/m^2 \cdot K$ ,
$R_c$ represents the contact resistance in $m^2 \cdot K/W$ ,