What is the ratio of the kinetic energies of mol-ecules to that of molecules in air at room tempera-ture? (b) What is the ratio of the rms speed of molecules to that of molecules in air at room tem-O2 O2 N2 perature? (c)Are these ratios temperature-dependent?
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(a) What is the ratio of the kinetic energies of $\mathrm{O}_{2}$ molecules to that of $\mathrm{N}_{2}$ molecules in air at room temperature? (b) What is the ratio of the $\mathrm{rms}$ speed of $\mathrm{O}_{2}$ molecules to that of $\mathrm{N}_{2}$ molecules in air at room temperature? (c) Are these ratios temperature-dependent?
Statistical Mechanics
Temperature
a) At what temperature do oxygen molecules have the same average speed as helium atoms $(M=4.00 \mathrm{g} / \mathrm{mol})$ have at $300 \mathrm{K}$ ? b) What is the answer to the same question about most probable speeds? $\mathrm{c}$ ) What is the answer to the same question about rms speeds?
a) Calculate the rms speed of an oxygen gas molecule (O2) at 31.0°C. b) At the same temperature, which molecule travels faster, O2 or N2? c) Using your answer to question 8b above, calculate how much faster? d) Standard Temperature is defined to be 273.15K. What is the average translational kinetic energy of a single molecule of an ideal gas at Standard Temperature? e) One mole (mol) of any substance consists of 6.022 x 10^23 molecules (Avogadro's number). What is the translational kinetic energy of 12.00 mol of an ideal gas at 300.0K? f) A sealed syringe contains 10 × 10^-6 m^3 of air at 1 × 10^5 Pa. The plunger is pushed until the volume of trapped air is 4 x 10^-6 m^3. If there is no change in temperature, what is the new pressure of the gas? g) A car tyre contains air at 1.25 × 10^5 Pa when at a temperature of 27°C. Once the car has been running for a while, the temperature of the air in the tyre rises to 42°C. If the volume of the tyre does not change, what is the new pressure of the air in the tyre?
Lainey R.
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