Answer:
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)