Finding initial and final temperatures

Question

Assignment:

Q1. Given that  s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56.

Q2. Solve log(2x + 3) = log(4x) + 2, for x giving the answer correct to 3 significant figures.

Q3. For a thermodynamic process involving a perfect gas, the initial and final temperatures are related by:

T₁ exp(^s/Cp) = T₂

Where Cp is the specific heat capacity of the gas, ^s is the change of entropy and T1 and T2 are the initial and final temperatures of the process. Determine the value of ^s (units - kJ/kg) if T1 = 320 K, T2 = 450K and Cp = 1.005 kJ/kg K.

Q4. Transform the formula

Y1  = X1

Y2     X2

To make n the subject.

Q5. Make y the subject of the formula:

E = P(1 - e(y - 1))

Q6. Given the complex numbers:

z1  = 5 - j4        z2 = 4 + j        z3 = -6 - j7         z4 = j2

Calculate, giving answers in the form a +jb, the following:

(i)  z4 - z1 + z2

(ii) 3z1 - 2z3 + z4

(iii) z1z2

(iv) z3/z2

Q7. Simplify each of the following giving your answer as a complex number in polar form:

(i) 12 / 40degrees  * /135degrees

(ii) 32 /-15 degrees     

8 / 48degrees  

(iii) 3 /120degrees * 4 / 30 degrees

5 / 24 degrees

Q8. (a) Convert the following to polar form giving the arguments in degrees:

(i) 4 - j2.4

(ii) -5.1 + j1.7

(b) Convert the following to polar form giving the arguments in radians:

(i) 1 + j3

(ii) 5 - j2

Q9. Convert the following complex numbers to rectangular (a + jb) form:

(i) 4.2(cos30degrees + j sin30degrees)

(ii) 5 / -124degrees

(iii) 2.6(cos pi/3 + j sin pi/3)

Q10. Show the following complex numbers on an Argand diagram:

(i) -6 + j5

(ii) 3 - j7

(iii) 7 /58degrees

Provide complete and step by step solution for the question and show calculations and use formulas.