Question
By using the differential dG = d(U + PV − ST),
(G = Gibbs free energy, P = pressure, V = volume, S = entropy
and T = temperature of system), and given that the internal energy U
satisfies dU = T dS − P dV,
derive a Maxwell relation connecting (∂V/∂T)P and (∂S/∂P)T .
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 4 steps
Knowledge Booster
Similar questions
- In free space, U (r, t) must satisfy tne wave equation, VU - (1/)U/at = 0. Use the definition (12.1-21) to show that the mutual coherence function G(r1,r2, 7) satisfies a pair of partial differential cquations known as the Wolf equations, 1 PG = 0 vG – (12.1-24a) vG - 1 G = 0, (12.1-24b) where V and V are the Laplacian operators with respect to r, and r2, respectively. G(rı, r2, 7) = (U*(r1,t) U(r2, t + T)). (12.1-21) Mutual Coherence Functionarrow_forwardFind the number density N/V for Bose-Einstein condensation to occur in helium at room temperature (293 K). Compare your answer with the number density for an ideal gas at room temperature at 1 atmosphere pressure.arrow_forwardFind a formula for the temperature of an Einstein solid in the limit q « N . Solve for the energy as a function of temperature to obtain U = N€e-€/kT (where € is the size of an energy unit).arrow_forward
- Explain the answer to the second and last equation in detailarrow_forwardOne-dimensional harmonic oscillators in equilibrium with a heat bath (a) Calculate the specific heat of the one-dimensional harmonic oscillator as a function of temperature (b) Plot the T -dependence of the mean energy per particle E/N and the specific heat c. Show that E/N → kT at high temperatures for which kT > hw In this limit the energy kT is large in comparison to hw , the separation between energy levels. Hint: expand the exponential function 1 ē = ħw + eBhwarrow_forwardFor a gas of nitrogen (N2) at room temperature (293 K) and 1 atmosphere pressure, calculate the Maxwell-Boltzmann constant A and thereby show that Bose-Einstein statistics can be replaced by Maxwell-Boltzmann statistics in this case.arrow_forward
arrow_back_ios
arrow_forward_ios