Classical Mechanics

Statistical Thermodynamics

Ideal gas law

         

Consider an oxygen gas with a volume of 1000 cm31000 \text{ cm}^3 at 45.0C45.0^\circ\text{C} and 1.03×105 Pa.1.03 \times 10^5 \text{ Pa}. If it expands until its volume is 1600 cm31600 \text{ cm}^3 and its pressure is 1.06×105 Pa,1.06 \times 10^5 \text{ Pa}, what is the approximate final temperature of the gas?

The value of the gas constant is R=8.31 J/molK.R=8.31 \text{ J/mol}\cdot\text{K}.

When the temperature is 0.00C,0.00^\circ\text{C}, a tire has a volume of 1.63×102 m31.63 \times 10^{-2} \text{ m}^3 and a gauge pressure of 170 kPa.170 \text{ kPa}. Assuming that the atmospheric pressure is 1.01×105 Pa,1.01 \times 10^5 \text{ Pa}, what is the approximate gauge pressure of the air in the tires when its temperature rises to 27.0C27.0^\circ\text{C} and its volume increases to 1.68×102 m3?1.68 \times 10^{-2} \text{ m}^3?

Suppose a cylinder containing 8 L8 \text{ L} of oxygen gas. The temperature and pressure of it is 20C20^\circ\text{C} and 12 atm,12 \text{ atm}, respectively. If the temperature is raised to 36C,36 ^\circ\text{C}, and the volume is reduced to 6.5 L,6.5 \text{ L}, what will be the approximate final pressure of the gas in atmospheres?

Assume that the gas is ideal.

If one mole of ideal gas expands at a constant temperature TT of 320 K320 \text{ K} from an initial volume ViV_i of 15 L15 \text{ L} to a final volume VfV_f of 19 L,19 \text{ L}, Approximately how much work is done by the gas during the expansion?

The value of the gas constant is R=8.31 J/molK.R=8.31 \text{ J/mol}\cdot\text{K}.

Suppose that 1.25×10141.25 \times 10^{14} particles traveling in the positive xx-direction in a vacuum chamber at a speed of 3.00×107 m/s3.00 \times 10^7 \text{ m/s} strike a circular target of radius 4.00 mm4.00 \text{ mm} during 4.00×108 s.4.00 \times 10^{-8} \text{ s}. The mass of each particle is 9.11×1031 kg.9.11 \times 10^{-31} \text{ kg}. What is the average pressure felt by the target, assuming that all the particles penetrate the target and are absorbed?

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