CALC (a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval υ to υ + Δ υ is Δ N = ∫ υ υ + Δ υ f ( υ ) d υ . (b) If Δ υ is small, then f ( υ ) is approximately constant over the interval and Δ N ≈ Nf ( υ )Δ υ . For oxygen gas (O 2 , molar mass 32.0 g/mol) at T = 300 K, use this approximation to calculate the number of molecules with speeds within Δ υ = 20 m/s of υ mp . Express your answer as a multiple of N . (c) Repeat part (b) for speeds within Δ υ = 20 m/s of 7 υ mp . (d) Repeat parts (b) and (c) for a temperature of 600 K. (e) Repeat parts (b) and (c) for a temperature of 150 K. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions agree with what is shown in Fig. 18.23?
CALC (a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval υ to υ + Δ υ is Δ N = ∫ υ υ + Δ υ f ( υ ) d υ . (b) If Δ υ is small, then f ( υ ) is approximately constant over the interval and Δ N ≈ Nf ( υ )Δ υ . For oxygen gas (O 2 , molar mass 32.0 g/mol) at T = 300 K, use this approximation to calculate the number of molecules with speeds within Δ υ = 20 m/s of υ mp . Express your answer as a multiple of N . (c) Repeat part (b) for speeds within Δ υ = 20 m/s of 7 υ mp . (d) Repeat parts (b) and (c) for a temperature of 600 K. (e) Repeat parts (b) and (c) for a temperature of 150 K. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions agree with what is shown in Fig. 18.23?
CALC (a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval υ to υ + Δυ is
Δ
N
=
∫
υ
υ
+
Δ
υ
f
(
υ
)
d
υ
. (b) If Δυ is small, then f(υ) is approximately constant over the interval and ΔN ≈ Nf(υ)Δυ. For oxygen gas (O2, molar mass 32.0 g/mol) at T = 300 K, use this approximation to calculate the number of molecules with speeds within Δυ = 20 m/s of υmp. Express your answer as a multiple of N. (c) Repeat part (b) for speeds within Δυ = 20 m/s of 7υmp. (d) Repeat parts (b) and (c) for a temperature of 600 K. (e) Repeat parts (b) and (c) for a temperature of 150 K. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions agree with what is shown in Fig. 18.23?
A)An ideal gas is confined to a container at a temperature of 330 K.What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.)
B)2.00 mol of the helium is confined to a 2.00-L container at a pressure of 11.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10−27 kg.Calculate vrmsvrms. (Express your answer to three significant figures.)
C)A gold (coefficient of linear expansion α=14×10−6K−1α=14×10−6K−1 ) pin is exactly 4.00 cm long when its temperature is 180∘∘C. Find the decrease in long of the pin when it cools to 28.0∘∘C? (Express your answer to two significant figures.)
The mean free path λ and the mean collision time T of molecules of a diatomic gas with molecular mass 6.00 x10^-25 kg and radius r=1.0x10^-10m are measured.From these microscopic data we can obtain macroscopic properties such as temperature T and pressure P? If yes, consider λ=4.32x10^-8m and T=3.00x10^-10s and calculate T and P.a)It's not possible.b)Yes,T=150K and P~2.04atm.c)Yes,T=150K and P~4.08atm.d)Yes,T=300K and P~4.08atm.e)Yes,T=300K and P~5.32atmf)Yes,T=400K and P~4.08atmg)Yes,T=400K and P~5.32atm.
The following figure is a histogram showing the speeds of the molecules in a very small gas. What are (a) the most probable speed, (b) the average speed, and (c) the rms speed?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.