Thermodynamics Homework Assignment: Equation of State and Specific Heat Capacities, Assignments of Thermal Physics

Download Thermodynamics Homework Assignment: Equation of State and Specific Heat Capacities and more Assignments Thermal Physics in PDF only on Docsity! HOMEWORK ASSIGNMENT 4 Problems Chapter 4 4-2 Given the equation of state and specific internal energy (P + b) v = RT, u = aT + bv + u0 a) What is cv? cv = ( ∂u ∂T ) v = a b) Show that cP − cv = R cP = ( ∂h ∂T ) P = ( ∂ (u + Pv) ∂T ) P = ( ∂u ∂T ) P = a + (b + P ) ( ∂v ∂T ) P = cv + ( ∂ ∂T RT ) P = cv + R 4-6 Oxygen gas has cv = 5R/2. Two moles are heated from 27 0C to 227 0C. a) The internal energy changes is ∆U = ncv∆T = 2 ∗ 5R2 ∗ 200 = 5 ∗ 8.31 ∗ 10 3 ∗ 200 = 8. 31× 106 J b) The enthalpy change is ∆H = ncp∆T = 2 ∗ 7R2 ∗ 200 = 7 ∗ 8.31 ∗ 10 3 ∗ 200 = 1. 16× 107 J 4-8 For an ideal gas, adiabatic expansion implies PV γ = constant, PV = nRT a) Eliminate P to get the relationship between V and T nRT V V γ = constant or TV γ−1 = another constant b) Eliminate V to get the relationship between P and T P ( nRT P )γ = constant = (nRT )γ P γ−1 or T P (γ−1)/γ = constant 1