In my first year of undergrad, I was given a great gift. I had the chance to meet regularly with a man I considered to be one of the best particle physicists in the country. The actual purpose of our meetings was to achieve competency doing Physics in his native language, but it became something altogether more valuable to me. Over several weeks, we worked through Schrödinger’s solution to the Hydrogen atom.

So…, “so” used as here needs to die. It adds nothing by its use but an air of aloof faux-intellectualism. It is not continuing a flow of thought. It is not communicating emphasis. It is superfluous and annoying. It is a faux so. It attempts to cast the hearer as a dumb dog eagerly awaiting the ball to leave the trainer’s hand at the time only of his knowing and choosing.

I don’t know what the future of cybersecurity consulting will be, but I have some thoughts. Back in the late 1900s, cybersecurity wasn’t really a thing. To the extent that it was, it was owned by a very small group who were both techy and a little naughty in the νοῦς, as they say. A typical cybersecurity engagement involved rocking up to a customer, him giving you a cable, and you going at it for love and money, getting pwns every which way before lunch.

AI is not just a buzzword. To be sure, as to the words, it is nonsense: there is no intelligence, but mere pattern matching and extrapolation. Well, call that intelligence if you will; I won’t. But the effects of AI cannot be downplayed and should not be ignored by anyone in a technical discipline not wanting to be left behind. If you work in any of these industries, I believe it’s very possible that AI is coming to eat your lunch:

An air conditioning device is working on a reverse Carnot cycle between the inside of a room at temperature \(T_2\) and the outside at temperature \(T_1\) > \(T_2\) with a monatomic ideal gas as the working medium. The air conditioner consumes the electrical power P. Heat leaks into the house according to the law \(\stackrel{.}{Q} = A(T_1 − T_2)\). Show that the efficiency of the air conditioner is \(η_{cool} = {T_2 \over T_1-T_2}\).

The Diesel cycle is the thermodynamic cycle which approximates the pressure and volume of the combustion chamber in a Diesel engine. In the Diesel cycle, the working medium in the combustion chamber is compressed adiabatically from \(V_1\), \(p_1\) to \(V_2\) < \(V_1\), \(p_2\) > \(p_1\), expanded isobarically at \(p_2\) from \(V_2\) to \(V_3\) > \(V_2\), expanded adiabatically from \(V_3\), \(p_2\) to \(V_1\) and \(p_4\) > \(p_1\), cooled isochorically at \(V_1\) from \(p_4\) to the initial pressure \(p_1\).

Many thanks to Bart Andrews for this contribution! Question Show that a relation of the kind \(f(x, y, z) = 0\) between the three quantities x, y, and z implies the relation \[\left(\frac{\partial x}{\partial y}\right)_z \left(\frac{\partial y}{\partial z}\right)_x \left(\frac{\partial z}{\partial x}\right)_y = -1\] between the partial derivatives. The grandcanonical partition sum \(Z_G\) is a function of the three parameters β, V, and μ. All other state variables are derived from \(Z_G\) and its partial derivatives.

Many thanks to Bart Andrews for this contribution! Question Consider a gas in contact with a solid surface. The molecules of the gas can adsorb to specific sites on the surface. These sites are sparsely enough distributed over the surface that they do not directly interact. In total, there are N adsorption sites, and each can adsorb n = 0, n = 1, or n = 2 molecules. When an adsorption site is unoccupied, the energy of the site is zero.

Many thanks to Bart Andrews for this contribution! Question Consider two systems \(I\) and \(II\) in contact with a common heat bath with temperature T and suppose that a mechanism exists which allows both systems to exchange particles. The probability that the composed system \(I + II\) is in a state for which system \(I\) has an energy between \(E_I\) and \(E_I+dE_I\) and a particle number \(N_I\), while \(II\) has an energy between \(E_{II}\) and \(E_{II} + dE_{II}\) with a particle number \(N_{II}\) is given by

Download as PDF. Question Consider a molecule, such as Carbon Monoxide, which consists of two different atoms, one Carbon and one Oxygen, separated by a distance \(d\). Such a molecule can exist in quantum states of different orbital angular momentum. Each state has the energy \[ \epsilon_l={\hbar^2 \over 2I}l(l+1)\] where \(I=\mu d^2\) is the moment of inertia of the molecule about an axis through its centre of mass and \(\mu\) is the reduced mass defined by \(\frac 1\mu=\frac{1}{m_1} + \frac{1}{m_2}\).