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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.

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 \(R=8.31 \text{ J/mol}\cdot\text{K}.\)

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 \(R=8.31 \text{ J/mol}\cdot\text{K}.\)

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