Exam 21: The Kinetic Theory of Gases

Air expands adiabatically (no heat in,no heat out)from T = 300 K and P = 100 atm to a final pressure of 1 atm.Treat the gas as ideal with γ = 1.4,and determine the final temperature.Compare your result to the boiling points of nitrogen (77.4 K)and oxygen (90.2 K).Could this method result in the liquification of air?

Assume 3.0 moles of a diatomic gas has an internal kinetic energy of 10 kJ.Determine the temperature of the gas after it has reached equilibrium.

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50°C.If the helium behaves like an ideal gas,the average kinetic energy per molecule is

If the total translational kinetic energy of the molecules of oxygen in a container is 15 J at room temperature,what is the total rotational kinetic energy of these molecules?

Five gas molecules are found to have speeds of 100,200,300,400,and 500 m/s.The rms speed (in m/s)is

According to kinetic theory,a typical gas molecule in thermal equilibrium at room temperature has a kinetic energy K = 6.00 × 10−²¹ J,regardless of mass.Estimate the speed at room temperature of a hydrogen molecule H₂ (m = 3.34 × 10−²⁷ kg)and a xenon atom (m = 2.00 × 10−²⁵ kg).[k_B = 1.38 × 10−²³ J/K]

Suppose a box contains about 5.0 × 10²¹ hydrogen atoms at room temperature (21°C).Determine the thermal energy of these atoms.

One mole of hydrogen,one mole of nitrogen and one mole of oxygen are held in a 22.4 × 10³ cm³ enclosed vessel at 20°C.The pressure in the vessel,in N/m²,is

A molecule in a uniform ideal gas can collide with other molecules when their centers are equal to or less than

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50°C.If the helium behaves like an ideal gas,the total energy of the system is

The internal energy of n moles of an ideal gas depends on

When we consider a thin horizontal layer of the atmosphere,of thickness dy,of area A,with pressure P on the bottom,with an average mass m per molecule,and n_V molecules per unit volume,the magnitude of the difference of the pressure at the top and bottom of the layer is given by dP =

Two tanks of gas,one of hydrogen,H₂,and one of helium,He,contain equal masses of gas.The gram-molecular mass of He is twice that of H₂.Both tanks of gas are at the same temperature,293 K.Which statement(s)below is(are)correct when we ignore vibrational motion?

Find the specific heat (in cal/mole K)of a gas kept at constant volume when it takes 1.0 × 10⁴ J of heat to raise the temperature of 5.0 moles of the gas 200 K above the initial temperature.

The average translational speed of a nitrogen molecule at room temperature (20°C)is approximately (in m/s)

The specific heat of an ideal gas at constant pressure is greater than the specific heat of an ideal gas at constant volume because

Which statement below is NOT an assumption made in the molecular model of an ideal gas?

When we say that the speed of sound is measured under adiabatic conditions we assume that