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Classical Mechanics

Statistical Thermodynamics

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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