entropy change calculator
Best Results From Yahoo Answers Youtube
From Yahoo Answers
Answers:Initially, we have two different solutions at different temperatures. Once they are mixed and equilibrated, the final state of the system is a homogeneous solution at some temperature intermediate between the initial temperatures of the two solutions. (I assume that the solutions are mixed in an insulated container, so that no heat is lost from the system during this process.) I will also assume that water and ethanol mix ideally, so that there is no net change in total volume of the solutions when they are mixed, and that the enthalpy of mixing is zero. There are two things going on here. First, there is an entropy change associated with equilibrating the temperatures of the two solutions. Second, there is an entropy change associated with the mixing of the two solutions. Because entropy is a function of state, we can choose to break apart the problem into tractable processes, so long as the initial and final states of the system correspond to the initial and final states noted above. First, calculate the equilibrium temperature of the combined system. Because this process occurs in a thermally isolated system, energy is conserved, and the heat energy gained by the cold water is equal to the heat lost by the hot ethanol. The heat capacity of a system is defined as C = dq/dT, T is the temperature, and q is the heat energy, so dq = C*dT If we assume the heat capacity is constant (doesn't depend on temperature), this integrates to: q = C* T In this question, the two solutions have different heat capacities, so we have: q_total = 0 = q_w + q_e = m_w*C_w*(T_eq - T_w) + m*e*C_e*(T_eq - T_e)) where q_w, m_w, C_w, and T_w are the change in heat, mass, specific heat capacity, and initial temperature of the water, and q_e, m_e, C_e, and T_e are the corresponding parameters for the ethanol. T_eq is the equilibrium temperature. Solving for T_eq gives: T_eq = (m_w*C_w*T_w + m_e*C_e*T_e)/(m_w*C_w + m_e*C_e) The equilibrium temperature is just the heat-capacity-weighted average of the temperatures of the two solutions. Plugging in the numbers for this problem gives: T_eq = (100gm*4J/(gm* C)*20 C + 50gm*2J/(gm* C)*80 C)J)/(100gm*4J/(gm* C) + 50gm*2J/(gm* C)) T_eq = 32 C This thermal equilibration is an example of an irreversible process, but because the entropy is a state function, it doesn't matter how we get to the final state. We can therefore use a reversible path to calculate the entropy changes, which simplifies things. We can calculate the entropy change involved in reversibly taking the water from T_w to T_eq, and add that to the entropy change involved in taking the ethanol from T_e to T_eq, and we will end up with the desired answer. For a reversible process: dS = dq/T But from above, we know that dq = C*dT, so: dS = C*dT/T If C is constant, S = C*ln(T_final/T_initial) In this case, the total entropy change is: S_thermal = S_e + S_w = m_w*C_w*ln(T_eq/T_w) + m_e*C_e*ln(T_eq/T_e) Note that in this case, we must express the temperatures in absolute terms (in kelvins) because we are dealing with actual temperatures, not just temperature changes. S_thermal = (100gm*4J/(gm* C))*ln(305/293) + (50gm*2J/(gm* C))*ln(305/353) S_thermal = 1.44 J/K. This would be the entropy change if the two solutions were brought into thermal contact in an insulated container, and allowed to thermally equilibrate, but not physically mix. The next step is to calculate the entropy change due to mixing. Assuming ideal mixing, for this 2-component system, the entropy of mixing is given by: S_mix = -n*R*[x_w*ln(x_w) + x_e*ln(x_e)] where n is the total number of moles of water and ethanol, R is the universal gas constant x_w is the mole fraction of water in the final mixture x_e is the mole fraction of ethanol in the final mixture Because this is just a 2-component system, x_w + x_e = 1, so x_e = 1 - x_w The molecular mass of water is 18.02 gm/mol and the molecular mass of ethanol (C2H5OH) is 46.07 gm/mol. The mass of water and ethanol in this problem therefore correspond to: n_w = 100gm/(18.02 gm/mol) = 5.55 mol n_e = 50gm/(46.07 gm/mol) = 1.08 mol n = n_w + n_e = 6.635 mol x_w = 5.55mol/(5.55 + 1.08)mol = 0.836 x_e = 1 - x_w = 0.164 We know that R = 8.314 J/(mol*K). Plugging all this into the expression for S_mix gives: S_mix = -(6.635 mol)*(8.314 J/(mol*K))*[0.836*ln(0.836) + 0.164*ln(0.164)] S_mix = 24.62 J/K The total entropy change upon mixing these solutions is given by the sum of the thermal entropy change and the entropy of mixing: S_tot = S_thermal + S_mix = 1.44 J/K + 24.62 J/K = 26.06 J/K. The answer you were given is incorrect.
Answers:1. Equilbrium G = H - T S, equlibrium gibbs free energy, G = 0 0 = H - T S S = H/T 2. Molecules movement are more order in solid state compared to liquid state, thus entropy of solid is lower. 3. Enthalpy of fusion of water is 6.009 kj/mol at 0 degrees Celsius It means for every 1 mol of water at 0 deg. C, water will release 6.009 kJ to change its phase to solid.
Answers:There is something that puzzles me about this question. if the process is adiabatic, the gas is being heated by compression (DeltaE = W since q = 0) and, as your reasoning correctly implies, the process is reversible and there is no change in entropy. You cannot heat a gas adiabatically at constant pressure, so I don't understand your reference to pressure of 1 atm.
Answers:a) For a reversible process, dS = q/T where q is the infinitesimal amount of thermal energy added to the system at temperature T from the surroundings. For an adiabatic process, q = 0, so dS = 0 and S(1->2) = 0 Nevertheless, we will need to know how the volume changed in this process so that we can express the total entropy change in terms of the initial and final states. Let the entropy be a function of volume and temperature, so S = S(V,T) Take the total differential of the entropy: dS = ( S/ V)_T dV + ( S/ T)_V dT Identify that ( S/ T)_V = Cv/T dS = ( S/ V)_T dV + (Cv/T) dT Using a Maxwell's Relation (see source), we can write ( S/ V)_T = ( P/ T)_V, so: dS = ( P/ T)_V dV + (Cv/T) dT For 1 mole of an ideal gas, we know that P = RT/V ( P/ T)_V = R/V So: dS = (R/V) dV + (Cv/T) dT Integrate: S = R*ln(V_final/V_initial) + Cv*ln(T_final/T_initial) We already know that S(1 -> 2) = 0, so: 0 = R*ln(V2/V1) + Cv*ln(T2/T1) R*ln(V2/V1) = Cv*ln(T1/T2) R*ln(V2) = Cv*ln(T1/T2) + R*ln(V1) ----------------- b) Go back to the expression we derived above: S = R*ln(V_final/V_initial) + Cv*ln(T_final/T_initial) This next path is specified to be isothermal, so dT = 0, and T_final = T_initial, (T2 = T3) and the temperature term is zero. S(2->3) = R*ln(V3/V2) = R*ln(V3) - R*ln(V2) --------------- c) Step 3 is another adiabatic process, so S(3->4) = 0 and 0 = R*ln(V4/V3) + Cv*ln(T4/T2) R*ln(V4/V3) = Cv*ln(T2/T4) R*ln(V3) = R*ln(V4) - Cv*ln(T2/T4) The total entropy change is S(1->4) = S(1->2) + S(2->3) + S(3->4) = 0 + R*ln(V3/V2) + 0 S(1->4) = R*ln(V3) - R*ln(V2) Plugging in the expressions we had above for ln(V2) and ln(V3) S(1->4) = R*ln(V4) - Cv*ln(T2/T4) - Cv*ln(T1/T2) - R*ln(V1) S(1->4) = R*ln(V4/V1) + Cv*ln(T4/T1) Note that because entropy is a state function, it doesn't matter what path we take to get from an initial state to a final state. We could have gotten to this result by taking a reversible path directly from state 1 to state 4 (T1,V1) to (T4, V4). Going back to our general expression for the entropy change for a reversible process: S = R*ln(V_final/V_initial) + Cv*ln(T_final/T_initial) Plug in state 4 for the final state and state 1 for the initial state, and we get: S(1 ->4) = R*ln(V4/V1) + Cv*ln(T4/T1)