. (40 points) Consider an insulated container of volume V2. N idea gas molecules are initially...
Thermodynamics Consider an insulated container of volume V2. N ideal gas molecules are initially confined within a sub-volume (V1) by a piston and the remaining volume V2 - Viis in vacuum. Let T., P., U1, S1, A1, H1, and G1 be the temperature, pressure, internal energy, entropy, Helmholtz free energy, enthalpy, and Gibbs free energy of the ideal gas at this state, respectively. Now, imagine that the piston is removed so that the gas has volume V2. After some time...
8. Initially, 1 mole of the real gas is contained in a thermally insulated piston-cylinder arrangement in an initial state (T1, P1, Vi ). 1 mole of the real gas that is expressed by the following equation of state under the investigation. Now, the gas is expanded so as to fill the final state of (T2, P2, V2 ). Suppose that any possible temperature dependence of Cy is negligibly small and the molar heat capacity is approximately equal to 2"...
Hydrogen in a fixed volume box placed in a heat bath will eventually io nize. At any one time you will have 3 particles in the box. Assuming a fixed number of protons and electrons, write an expression for Helmholtz free energy as a function of 7, V.NH, lingt, at- and any necessary constants. You may treat each constituent as an ideal gas. Hints: You will need this form of Sackur-Tetrode (although you'll need to account for mixed state entropy)...
5. Consider the following piston-cylinder arrangement which is thermally insulated. Initially, the same 1 mole of monoatomic ideal gas are confined in the cylinder A and B respectively which are partitioned by a thermally conducted metal plate as shown in Figure 1. The initial volume and absolute temperature (X) of two partitions are the same as V and T respectively and the external pressure of the cylinder is given by P, as shown in Figure 1. When heat (g) was...
5. (11 marks total) A well-insulated rigid container is subdivided by a partition into two parts A and B, each of volume V,- = 0.2 m, and each filled with air. The initial temperatures and pressures are P,, = 200 kPa, T.,-100°C, P,-100 kPa, and TB,-20°C. The partition is then removed, and the system comes to equilibrium. (a) (7 marks) Determine the final temperature and pressure in the container (b) (4 marks) Calculate the total entropy change for the air...
Initially, at a temperature T, and a molar volume vi, a van der Waals gas undergoes a change of state to the final temperature T2 and the molar volume V2. The van der Waals gas is characterized by the two parameters a and b (cf. Eq. (3.3)). a. Show that the change in molar entropy is As = c, In 72 + R In º2 = (3.62) 01 - 6 b. A volume of 1 dm is partitioned by a...
105Pa, initial temperature T-300K, and an initial 1. An ideal gas with initial pressure 2 volume V - 1m3 expands isothermally to a final volume of 2m3. Then, the gas returns to its initial state, first by constant pressure (isobaric) contraction, and then by a change at constant volume (isochoric) a) Draw a PV diagram of this process. What's the total change in thermal energy of the entire process? b) What's the work done by the environment on the gas?...
A monatomic ideal gas is initially at volume, pressure, temperature (Vi, Pi, Ti). Consider two different paths for expansion. Path 1: The gas expands quasistatically and isothermally to (Va, Pz. T2) Path 2: First the gas expands quasistatically and adiabatically (V2, P.,T-),where you will calculate P T. Then the gas is heated quasistically at constant volume to (Va. P2 T1). a. Sketch both paths on a P-V diagram. b. Calculate the entropy change of the system along all three segments...
6. The formula dS = dQ/T makes it look like a system can only increase its entropy by absorbing heat. You must however remember that this equation is only true for reversible processes. Entropy can change for a system without absorbing any heat. Consider the following scenario. You are given an insulated container with two compartments. The whole container is at the temperature T which remains constant. One compartment has a volume V1 and has n1 moles of an ideal...
02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature T. a) Consider entropy S = S(T, V) and derive the equation TdS. Tas = Cvat +T (1) dV. V Show that this equation can be written as follows BT TdS = CydT + PDV where Cv is the thermal capacity at constant volume, B is the isobaric expansiveness and K is isothermal compressibility: b) Consider a gas described by the equation of state...