## Solving Expressions Analytically Consider the following equation, which describes the speed of sound a in an ideal gas: a=kRT−−−−√. The Mach

Question

Solving Expressions Analytically Consider the following equation, which describes the speed of sound a in an ideal gas: a=kRT−−−−√. The Mach number M describes the ratio of a velocity v to the acoustic velocity or speed of sound a: M≡va. The Mach number can also be written in terms of the stagnation temperature T0, M=2k−1(T0T−1)−−−−−−−−−−−−−√. Combine these equations and solve symbolically for the temperature T in terms of all other quantities except M. Your answer should be stored in a variable T_result, which will be a list containing one or more sympy expressions. Prefer T0 instead of T_0 in this case.

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5 months 2021-08-14T00:50:40+00:00 1 Answers 42 views 0

T = (2k + 1)/(v^2kR + T0)

Explanation:

There are 3 equations

a = √kRT —— eqn (i)

M = va ——– eqn (ii)

M = √2k – 1(T0T – 1) —- eqn (III)

Substitute the expression of a in eqn (i) in eqn (ii)

eqn (ii) becomes M = v√kRT.

Equate this equation with eqn (iii) because M = M

v√kRT = √2k – 1(T0T – 1)

square both sides to eliminate the square root

v^2(kRT) = 2k – 1(T0T – 1)

v^2kRT = 2k – T0T + 1

v^2kRT + T0T = 2k + 1

T(v^2kR + T0) = 2k + 1

T = (2k + 1)/(v^2kR + T0)