6. a. Prove that every polynomial of degree k, p(n) = aknk + ak−1nk−1 + ... + a0 with ak > 0, belongs to (nk). b. Prove that exponential functions an have different orders of growth for different values of base a > 0.
Q: 1. What is the final thermal energy of the gas A? Express your answer to two significant figures and…
A:
Q: A cubic equation of state always has three roots, in which O Above the critical temperature Tc, two…
A: Here, we have to choose the right option regarding the three roots in the cubic equation of state.…
Q: (a)If Ideal gas molecules do not collide,these molecules will do [] A. uniform motion in A straight…
A: (a) Ideal gas molecules which are not under influence of external forces will never exhibit simple…
Q: What is the rms speed (in m/s) of a helium-3 atom in an ideal gas at a room temperature of 300…
A: Atom : Helium - 3 Temperature (T)= 300 k mass (m) = 3.016 u 1 u = 1.66×10-27 kg kB = 1.38×10-23 Jk
Q: A) System: N oscillators and q = 1. Calculate the number of microstates. B) System: N = 3; q = 4.…
A:
Q: 9. Molecular diffusion coefficients are typically mechanical dispersion coefficients O higer than O…
A: In general mechanical dispersion coefficients are much grater or higher than molecular dispersion…
Q: 111. What is the change in internal energy of the gas? a. 2.56 x 104 J b. 1.28 x 105 J AV = ncpAT c.…
A: Number of moles n = 7 Change in the temperature ∆T = 1172.60 k Specific heat at constant volume…
Q: 5 mole of an ideal vibrating diatomic gas. What is the heat capacity at constant volume in J/K?
A: Given that The number of the mole is (n) = 5 As we know that the Number of the degree…
Q: piston mA ideal gas A movable piston (mass = m and cross-sectional area = A) holds 0.5 mol of an…
A:
Q: 9. Diffusion across a one-dimensional slab C₁=Co x=0 a) C. (z) b) Ci(z) = c) C₁(z) = d) C.(z)=(1-1)…
A:
Q: Learning Goal: To understand the ideal gas law and be able to apply it to a wide variety of…
A:
Q: i. ii. iii. A mole of an ideal gas of vibrating diatomic molecules at initial temperature Ti is…
A:
Q: 2. Find the steady-state temperature distribution u in a solid semi-infinite cylinder of radius a if…
A: Concept: Given Boundary Condition are u=0 at r=1u=rsinθ at z=0Consideringu=R(r) Θ(θ)…
Q: Р (Рa) 800 600 400 A C 200 2 8 10 v (m) 4 6 le of an ideal gas is taken through a closed cycle…
A: Given:
Q: 7. Under which of the following conditions would you expect real gases to approach ideal behavior?…
A: If particles are moving faster, they are more likely to collide with the container walls. This…
Q: Use the Gibbs expression for entropy (eqn 14.48) to derive the formula for the entropy of mixing…
A:
Q: A gas sample enclosed in a rigid metal container at room temperature (20.0°C) has an absolute…
A: We know that the ideal gas law is PV = nRT P= pressure V= Volume n = mole no R =molar gas…
Q: A process at constant volume pressure takes n mole vibrating diatomic from an initial temperature T…
A: initial temperature = T.final temperature = 3T.for diatomic molecule the degree of freedom for both…
Q: How would I draw the following graphs for a simple ohmic device from the equations V=IR and…
A: A device that obeys Ohm's Law for all voltages across it under constant physical conditions such as…
Q: Constant amount of ideal gas is kept inside a cylinder by a piston. Then the gas expands…
A:
Q: 3. The specific Helmholtz Free energy f is related to the specific internal energy u as: f (T, a) =…
A:
6. a. Prove that every polynomial of degree k, p(n) = aknk + ak−1nk−1 + ... + a0
with ak > 0, belongs to (nk).
b. Prove that exponential functions an have different orders of growth for
different values of base a > 0.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- In the Taylor Expansion, it looks like they've made x_0 = x_1, x_2 and made x = x_1 - a, x_2 - a. I don't understand how they can use that substitution for x_0 since it is a constant, and x_1 and x_2 are variables that can change.D). i.,ii.,iii. Please!Learning Goal: To understand the ideal gas law and be able to apply it to a wide variety of situations. The absolute temperature T, volume V, and pressure p of a gas sample are related by the ideal gas law, which states that PV = nRT Here n is the number of moles in the gas sample and R is a gas constant that applies to all gases. This empirical law describes gases well only if they are sufficiently dilute and at a sufficiently high temperature that they are not on the verge of condensing. In applying the ideal gas law, p must be the absolute pressure, measured with respect to vacuum and not with respect to atmospheric pressure, and I must be the absolute temperature, measured in kelvins (that is, with respect to absolute zero, defined throughout this tutorial as -273°C). If p is in pascals and V is in cubic meters, use R = 8.3145 J/(mol · K). If p is in atmospheres and V is in liters, use R = 0.08206 L atm/(mol-K) instead. Part A A gas sample enclosed in a rigid metal container at…
- 3. The specific Helmholtz Free energy f is related to the specific internal energy u as: f(T, a) = u - Ts where the "natural variables" of fare temperature and specific volume. a. Expand the differential off in terms of partial derivatives with respect to the natural variables of f b. Using the result from a. and applying the 1st Law of Thermodynamics, what are af af Tand да ila? ap c. From the equality of mixed partial derivatives, show that ƏT = Əs θα |T5. For a system, the thermodynamic as)vn energy U is defined as a function of S, V, and n which is U(S,V,n) = kn3V 3e3nR %3D where S is the entropy, V is the volume, n is the number of moles, K is the constant, and R is the gas constant. Determine a. Based on the theory in Thermodynamics, (), T = Determine, b. Based on the theory in Thermodynamics, Pressure P = . S,n 5/8 Determine c. Determine ne d. Determine dU in dS, dV and dn* ? 63. During isothermal compression, the internal energy of an ideal gas : a. Decreases b. Can go either way depending on the precise pressures and volumes c. Stays the same d. Increases 64. What is the total internal energy of a sample of 9 moles of air (considered as an ideal gas) at a temperature of 3°C? Assume that the rotational degrees of freedom are fully activated, and that the vibrational modes are "frozen out". (k=1.38 x 10-23 J/K, N-6.022x10²3) 3°C = 273+3 = 276 U= n NAF ( 1₂ KT) (9)(6.022 X 10²²) x 1.38×10²³ x 276) = 1032 a. 1.19 x 105 J b. 9.29 x 104 J c. 7.23 x 104 J d. 5.16 x 104 J 65. What is the average translational kinetic energy per oxygen molecule in this sample? a. 1.2 x 10-20 J b. 9.14 x 10-21 J c. 5.71 x 10-21 J d. 1.54 x 10-20 J 66. Is this kinetic energy the same or different from the nitrogen molecules in the sample? a. Different b. The same 67. What is the rms speed of the oxygen molecules in this sample? (the atomic mass number of oxygen is 15.994, 1 u =…