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# Statistical Thermodynamics

Entropy is the least understood quantity in science, as are the laws that govern it. Avoid the pitfalls and understand entropy better than most working scientists.

# Ideal gas law

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

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

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

Suppose a cylinder containing $$8 \text{ L}$$ of oxygen gas. The temperature and pressure of it is $$20^\circ\text{C}$$ and $$12 \text{ atm},$$ respectively. If the temperature is raised to $$36 ^\circ\text{C},$$ and the volume is reduced to $$6.5 \text{ L},$$ 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 $$T$$ of $$320 \text{ K}$$ from an initial volume $$V_i$$ of $$15 \text{ L}$$ to a final volume $$V_f$$ of $$19 \text{ L},$$ Approximately how much work is done by the gas during the expansion?

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

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

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