{\displaystyle F} The three states of matter: solid, liquid, and gas. {\displaystyle t} The phase angle is the characteristic of a periodic wave. {\displaystyle F} {\displaystyle F} [ $, $ \begin{matrix}\frac{\pi }{2} \end{matrix} $, $ A(t)\cdot \sin[2\pi ft + \phi(t)] = I(t)\cdot \sin(2\pi ft) + Q(t)\cdot \underbrace{\cos(2\pi ft)}_{\sin\left(2\pi ft + \begin{matrix} \frac{\pi}{2} \end{matrix}\right)} $, $ A(t)\cdot \cos[2\pi ft + \phi(t)] = I(t)\cdot \cos(2\pi ft) \underbrace{- Q(t)\cdot \sin(2\pi ft)}_{+ Q(t)\cdot \cos\left(2\pi ft + \begin{matrix} \frac{\pi}{2} \end{matrix}\right)} $, $ I(t)\ \stackrel{\mathrm{def}}{=}\ A(t)\cdot \cos[\phi(t)], \, $, $ Q(t)\ \stackrel{\mathrm{def}}{=}\ A(t)\cdot \sin[\phi(t)].\, $, $ \begin{matrix} \frac{\pi}{2} \end{matrix} $. t 4 The number of bonds is proportional to the number of molecules and thus to the mass of the sample. One complete cycle of the wave has 360º of phase angle in the Cartesian plot.

{\displaystyle G} [ Figure \(\PageIndex{2}\) shows the result, as well as showing a familiar example of sublimation. {\displaystyle F}

They pass a point at different instants in time. {\displaystyle t} If heat is added, some of the solid will melt, and if heat is removed, some of the liquid will freeze. $ x(t) = A\cdot \sin( 2 \pi f t + \theta ),\, $, $ \begin{matrix} \frac{1}{4} \end{matrix}\, $, $ x(t - \begin{matrix} \frac{1}{4} \end{matrix}T) \, $, $ = A\cdot \sin(2 \pi f (t - \begin{matrix} \frac{1}{4} \end{matrix}T) + \theta) \, $, $ = A\cdot \sin(2 \pi f t - \begin{matrix}\frac{\pi }{2} \end{matrix} + \theta ),\, $, $ \theta - \begin{matrix}\frac{\pi }{2} \end{matrix}. ( Then the phase of [

However, in a phase transition, heat transfer does not cause any temperature change. Does it make sense? For water, the triple point occurs at \(273.16 \, K \, (0.01^oC)\) and 611.2 Pa; that is a more accurate calibration temperature than the melting point of water at 1.00 atm, or \(273.15 \, K \, (0.0^oC)\). At this equilibrium, if heat is added, some of the liquid will evaporate, and if heat is removed, some of the gas will condense; molecules either join the liquid or form suspended droplets. Thus, the two variables (pressure and temperature) can be changed independently, and the same phase assemblage continues to exist.

t

Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic motion. {\displaystyle +\pi } But the time difference (phase difference) between them is a constant - same for every pass since they are at the same speed and in the same direction. t

F If the frequencies are different, the phase difference Such a pT graph is called a phase diagram. Solve the appropriate equation for the quantity to be determined (the unknown). )

F ( This prevents the temperature inside the orange from dropping below freezing, which would damage the fruit (Figure \(\PageIndex{6}\)). be a periodic signal (that is, a function of one real variable), and

{\displaystyle T} When the temperature and pressure of a pure substance are fixed, the equilibrium state of the substance is also fixed.

) t is. Complete cancellation is possible for waves with equal amplitudes. The ice and liquid water are in thermal equilibrium, so that the temperature stays at the freezing temperature as long as ice remains in the liquid. F

If the two frequencies were exactly the same, their phase relationship would not change and both would appear to be stationary on the oscilloscope display.

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