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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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