The Gibbs function of a particular gas is G = nRT In(P) - AP² + B Where A and B are constants. Find expression for (i) The entropy S of the gas (ii) The volume V of the gas (iii) The equation of state of the gas
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- Problem 1: Describe a situation in which the entropy of a container of gas is constant. In other words, come up with your own problem where the answer is that AS = 0.We trapped 28 kg of dry air, and it initially has standard pressure and temperature. The trapped air parcel rises in the atmosphere until the temperature is 188 K. What is the change in entropy if the pressure decreases by 28% after the parcel rises?A 23.9 g block of copper whose temperature is 382 K is placed in an insulating box with a 57.3 g block of lead whose temperature is 228 K. (a) What is the equilibrium temperature of the two-block system? (b) What is the change in the internal energy of the two-block system between the initial state and the equilibrium state? (c) What is the change in the entropy of the two-block system? The heat capacities of copper and lead are 386 J/kg-K and 128 J/kg-K, respectively. (a) Number i (b) Number i (c) Number i Units Units Units
- Consider 4.00 mol of an ideal gas with a constant‑volume molar specific heat of 12.5 J/(mol·K), an initial temperature of 26.8 ∘C, and an initial pressure of 5.710×104 Pa. The state of the gas is then changed to a final temperature of 48.1 ∘C and a final pressure of 3.090×104 Pa. What is the change in the entropy Δ? of the gas during this process? The gas constant is 8.31 J/(mol·K).When a metal bar is temporarily connected between a hot reservoir at Th and a cold reservoir at Tc, the energy transferred by heat from the hot reservoir to the cold reservoir is Qh. In this irreversible process, find expressions for the change in entropy of the following. (Use any variable or symbol stated above as necessary.) (a) the hot reservoir ΔSh = (b) the cold reservoir ΔSc = (c) the Universe ΔSU =By considering the number of accessible states for an ideal two-dimensional gas made up of N adsorbed molecules on a surface of area A, obtain an expression for the entropy of a system of this kind. Use the entropy expression to obtain the equation of state in terms of N, A, and the force per unit length F. What is the specific heat of the two-dimensional gas at constant area?
- Consider the adiabatic free expansion of n moles of an ideal gas from volume V₁ to volume V2, where V₂ > V₁. [Hint: check lecture 19, chapter 5.6, process number 5. Note that such a process happens quasi-instantaneously, thus, it is irreversible.] (1) Calculate the change in entropy of the gas. (2) Calculate the change in entropy of the environment. (3) Evaluate the total change in entropy (AS = ASgas + ASenv.) for 1 mole, with V₂ = 2V/₁.A box contains 100 gas molecules all released on the left side of the box. What is the initial entropy of all the gas molecules on one side? You can calculate the number of microstates (left/right distribution of molecules) possible by the equation W = N! / ( nL! * nR!,) where N is the total number of molecules and nL is the number on the left and nR is the number on the right. What is the entropy of the most disorganized distribution of gas molecules?