Tutor profile: Jonathan F.
Subject: Physics (Thermodynamics)
Consider a water-oil system. If water molecules disperse into oil, it will lead to a higher entropy for the system. However, water molecules instead agglomerate into droplets, with little or no water dissolved into the oil phase. Since processes usually tend to go to higher entropy, why does that happen?
According to Gibbs' free energy, processes can be spontaneous even if they are not entropically favorable if they are highly energetically favorable. This can be seen analyzing the equation dG = dH - TdS, where G is the Gibbs' free energy, H is the enthalpy, T is the temperature and S is the entropy. For an entropically unfavorable process to happen spontaneously, the decrease in enthalpy (dH) must upset the increase in entropy times the temperature (TdS). In our system, water molecules agglomerate into droplets because that way they reduce the potential energy due to the interactions between hydrogen bonds. This leads to a highly energetically favorable process that happens spontaneously.
Subject: Physics (Newtonian Mechanics)
Two objects with masses m1 and m2, where m1 > m2, are thrown upwards from the surface of the Earth at the same initial speed. Which object will reach the ground first?
They reach the ground at the same time since the acceleration acting on both objects is the same, the gravitational acceleration (approximately 32.2 ft/sec2), and it is independent of the mass of the object. However, the object with mass m1 will require higher initial momentum to attain the same initial speed of the object with mass m2.
Two functions F and G are defined with domains D(F) and D(G). What is the domain of F/G?
The domain of F/G is the intersection of D(F) and D(G), excluding te values from which G is equal to zero since F/G does not exists for G = 0.
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