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
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. (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?
Chapter 18 Solutions
University Physics with Modern Physics (14th Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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