A rigid cylinder (15 cm radius, 15 cm height) contains nitrogen gas (N₂) at standard temperature and pressure (0 °C and 1 atm). What is the total translational kinetic energy of the gas molecules in the cylinder?

Question

Quizplus · Accepted Answer

The total translational kinetic energy of the gas molecules in the cylinder is given by:$$K = \frac{3}{2}NkT$$where:* $N$ is the number of molecules in the cylinder* $k$ is the Boltzmann constant* $T$ is the temperature in KelvinThe number of molecules in the cylinder can be calculated using the ideal gas law:$$PV = NkT$$where:* $P$ is the pressure in Pascals* $V$ is the volume in cubic metersSubstituting the given values into the ideal gas law, we get:$$(1 	ext{ atm})(0.00283 	ext{ m}^3) = N(1.38 	imes 10^{-23} 	ext{ J/K})(273 	ext{ K})$$$$N = 6.02 	imes 10^{23} 	ext{ molecules}$$Substituting the values of $N$, $k$, and $T$ into the equation for the total translational kinetic energy, we get:$$K = \frac{3}{2}(6.02 	imes 10^{23} 	ext{ molecules})(1.38 	imes 10^{-23} 	ext{ J/K})(273 	ext{ K})$$$$K = 1.6 	ext{ kJ}$$Therefore, the total translational kinetic energy of the gas molecules in the cylinder is 1.6 kJ.

A Rigid Cylinder (15 Cm Radius, 15 Cm Height) Contains