Solve algebraically for Q t PCL2h lnQQ 2hTf TinfinitySolu

Solve algebraically for Q: t = PCL/2h ln(Q/Q - 2h(T_f - T_infinity)

Solution

t =(pcL/2h)ln(Q/(Q-2h(T_f -T)))

write in reverse order

((pcL)/(2h))ln(Q/(Q-2h(T_f -T))) =t/1

cross multiply

ln(Q/(Q-2h(T_f -T)))*1=t((2h)/(pcL))

ln(Q/(Q-2h(T_f -T)))=((2ht)/(pcL))

lna=b =>a=e^b

(Q/(Q-2h(T_f -T)))=e^{((2ht)/(pcL))}

(Q/(Q-2h(T_f -T)))=e^{((2ht)/(pcL))}/1

cross multiply

Q=(Q-2h(T_f -T))e^{((2ht)/(pcL))}

(a-b)*c =a*c -b*c

Q=Qe^{((2ht)/(pcL))} -2h(T_f -T)e^{((2ht)/(pcL))}

2h(T_f -T)e^{((2ht)/(pcL))}=Qe^{((2ht)/(pcL))}-Q

write in reverse order

Qe^{((2ht)/(pcL))}-Q =[2h(T_f -T)e^{((2ht)/(pcL))}]

Q[e^{((2ht)/(pcL))}-1] =[2h(T_f -T)e^{((2ht)/(pcL))}]

Q =[2h(T_f -T)e^{((2ht)/(pcL))}]/[e^{((2ht)/(pcL))}-1]