교과서 질문
At 25 °C (approximately room temperature) the rms velocity of an Ar atom in air is 1553 km/h. (c) What is the total kinetic energy of 1 mol of Ar atoms moving at this speed?
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7. Gases
Kinetic Energy of Gases
객관식
Which of the following gases would have molecules with the greatest average kinetic energy at 25°C?
A
All have the same average kinetic energy
B
Helium (He)
C
Oxygen (O_2)
D
Nitrogen (N_2)
검증된 단계별 안내1
Recall that the average kinetic energy of gas molecules depends only on the temperature and is independent of the type of gas. This is a key concept from the kinetic molecular theory.
Write down the formula for the average kinetic energy per molecule: \(\text{KE}_{avg} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in kelvin.
Convert the given temperature from Celsius to kelvin using \(T(K) = T(^\circ C) + 273.15\). For 25°C, this becomes \(25 + 273.15 = 298.15\) K.
Note that since \(k_B\) is a constant and \(T\) is the same for all gases, the average kinetic energy \(\text{KE}_{avg}\) will be the same for helium, oxygen, and nitrogen at 25°C.
Conclude that all gases at the same temperature have the same average kinetic energy regardless of their molecular masses or identities.
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