Represent in coordinates p-v and T-s the transformation for which a system receives heat but lowers its temperature. Explain why this is possible.
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1. (a) Write the total differentials of s-S(V, T),S- S(P, T). Get used to it. This is the first step in many derivations in thermodynamics. We'll actually come back to these particular ones in the next lecture or so. (b) Now, from the 1st law we know that du dq+ dw. () Take the differential along a reversible path: dU - dgrev+ dwre. [Question: why don't we write dUrev? Yes, you must answer this and the other questions in blue.]...
7. Let V be the space generated by the basis B = {sin(t), cos(t), et}. i.e. V = span(B). Consider the linear transformation T:V + V defined by T(f(t)) = f"(t) – 2f'(t) – f(t). Find the standard matrix of the transformation. (Hint: Associate sin(t) with the vector (0), and so forth.) 8. Show that B = {t2 – 2, 3t2 +t, t+t+8} is a basis for P2, and find the change of coordinates matrix P which goes from B...
Thermodynamics: Draw Carnot diagram for T-S and P-V for engine heat for T1= 500 K and T2= 300 K.
Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T is the translated set T(p) + T(S) n R What would be the first step in translating p+ S? OA. Rewrite p+ S so that it does not use sets. O B. Rewrite p+S so that it does not use vectors O c. Rewrite p + S as a difference...
2 In the block diagram below, G(s) -1/s, P(s)P(s) s-+2 s+2 D(s)- k-oo Ше-ks[1-e-s/1001. The inverse Laplace transforms of these equations are g(t), p(t),p(t), and d(t), respectively. The parameter K scales the feedback k-0 D(s) R(s) G(s) P(s) C(s) P(s) A Consider for a moment, D(s)- 0. Simplify the block diagram in terms of G(s), P(s), P(s) and find the transfer function by substituting the equations given above B What are the zeros and poles of the system you obtained...
Question 10 on the P-v diagram shown, the dashed lines represent P-v diagram of a pure substance Lines of constant temperature Lines of constant pressure Lines of constant volume Saturated liquid curve Click Submit to complete this assessment
For an internal now, at location 11.-100°C and T.-120C. At location 2 T-132°C and T p 2 C What type of heat transfer process is occurring? Constant surface temperature? Constant flu? Not enough information is provided 6 12 ptj For the conditions described in problem S, is the flow fully developed or not? Explain to receive credit 7 12 pij Dos the fow over s lat plate over become t thermally fully developed? Explain to receive credit 8)12 p Is...
Isotherms Adiabatic process T. Figure 1 5. Given is the P-V diagram, a gas system from state is undergoing a thermodynamic process which lead to a different state f. Assume the gas is monoatomic and following the ideal gas condition ) Show that the, area under i-flineP 1-7 i) If the system contains 5 mol of this gas with an initially temperature of 293 1 m3 to Vi K. Calculate the work done by the system expanding from V -4m3...
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?...
Find the matrix [T], p of the linear transformation T: V - W with respect to the bases B and C of V and W, respectively. T:P, → P, defined by T(a + bx) = b - ax, B = {1 + x, 1 – x}, C = {1, x}, v = p(x) = 4 + 2x [T] C+B = Verify the theorem below for the vector v by computing T(v) directly and using the theorem. Let V and W...