Thermal/statistical physics:
a gas of interacting particles has an equation of state and heat capacity at constant volume given by the expression:
p(v, t)=a_{1}t^\frac{5}{2}+a_{2}t^3 +a_{3}v^-2 , c_{v}(t, v)=b_{1}vt^\frac{3}{2}+b_{2}t^2v+b_ {3}t^\frac{1}{2} where ai and bi are constants independent of t and v
find:
1.) the differential of internal energy in terms of dt and dv.
2.) the relationship between (some of) ai and bi due to the fact that u(t, v) is a function of state.
3. ) u(t, v) as a function of t and v.

What term do psychologists use to designate our personal awareness of feelings, sensations, and thoughts?

Argon is adiabatically compressed from an initial volume of 16 liters to a final volume of 2 liters. by what factor do the following quantities change? do they increase or decrease? (a) the rms speed (b) the thermal energy of the gas (c) the molar specific heat cv (d) the pressure

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)