(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?

2046.37 kPa

Explanation:

Given:

Number of moles, n = 125

Temperature, T = 20° C = 20 + 273 = 293 K

Radius of the cylinder, r = 17 cm = 0.17 m

Height of the cylinder, h = 1.64 m

thus,

volume of the cylinder, V = πr²h

= π × 0.17² × 1.64

= 0.148 m³

Now,

From the ideal gas law

we have

PV = nRT

here,

P is the pressure

R is the ideal gas constant = 8.314  J / mol. K

thus,

P × 0.148 = 125 × 8.314 × 293

or

P × 0.148 = 304500.25

or

P = 2046372.64 Pa = 2046.37 kPa

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