Question

question 15 (1 point)
the absolute temperature of an ideal gas is directly proportional to which of the following quantities?

a) the average speed of its molecules

b) it is proportional to all of the above quantities.

c) the mass of its molecules

d) the average momentum of its molecules

e) the average kinetic energy of its molecules

Explanation:

To solve this, we recall the kinetic theory of gases. The absolute temperature \( T \) of an ideal gas is directly proportional to the average kinetic energy (\( KE_{\text{avg}} \)) of its molecules. The formula is \( KE_{\text{avg}}=\frac{3}{2}kT \) (where \( k \) is Boltzmann's constant).

• Option a: Average speed (\( v_{\text{rms}}=\sqrt{\frac{3kT}{m}} \)) depends on mass (\( m \)) too, so not directly proportional to \( T \) alone.
• Option b: False, as seen from other options.
• Option c: Mass of molecules is independent of temperature.
• Option d: Average momentum (\( p = mv \)) depends on mass and speed, not directly proportional to \( T \) alone.
• Option e: Matches the kinetic theory relation.

Answer:

e) the average kinetic energy of its molecules