1. ,
L - ( ), - , . dt dL. . , :
dL/dt = - BL, dL = - BLdt, dL/L = - Bdt, ∫dL/L = - B∫dt
lnL = - Bt + lnC, lnL - lnC = -Bt, lnL/C = - Bt, L = Ce-Bt.
t = 0, = L0, L = L0 e-Bt.
2. .
L - . - , . Q - . :
dL/dt = Q -BL, dL (Q BL) = dt, ∫dL/(Q BL) = ∫ dt. Q - BL = , dy = -BdL, dL = - dy/B, 1/B∫dy/y =∫dt, ∫dy/y = - B∫dt
ln y = -Bt + lnC, ln y ln C = -Bt, ln y/C = -Bt, y = C * e-Bt.
Q - BL: Q - BL = * e-Bt.
t = 0, L = 0, = Q, Q - BL = Q * e-Bt, BL = Q - Q * e-Bt, BL = Q(l - e)-Bt,
L = Q/B(l - e-Bt).
3. , 10% . , . , 1 12 . .
- .
- t = 0.
- ,
t = 72 .; C = 0/2
C1 = 0,1
n -?
1. () :
dC/dt = -KC, dC/C = -Kdt, ∫ dC/C = -K∫dt,
In = -Kt + In , - ,
lnC - lnA = -Kt, InC/A = -Kt, C=A * e-Kt
t = 0, = 0, C0 = A * e-K0, A = C0, C = C0 * e-Kt.
2. , = C0/2 t =72
C0/2 = C0 * e-72K, 1/2 = e-72K, 2 = e72K, ln2 = 72K, K = 0.693/72, K =0.00962.
3. , : 1 =0,1 0.
0,10 = * e-0.09625t, 0,1 = -0.0096251, ln10 = e-0.009625', ln 10 = 0,009625t
ln 10 = 2,32, 3 = 0,009625t, t = 2.3/0.009625 = 240 () = 4 , n = 24/4 = 6 ( ).
4. 20f , 150 . . , .
= 36,6
= 20 -
= 15
-
= 0,0069 -1 -
|
|
t -?
dT/dt = -K(T TB), ∫dT/(T TB) = -K∫dT, ln(T TB) = -kT + lnC,
ln((T TB)/C) = -Kt, T TB = C * e-Kt, T = TB + C * e-Kt.
t = 0, T = T0, C = T0 TB.
= , = B + ( - B) * e-Kt, : 20 = 15 + 21,6 * e-Kt,
eKt = 21.6/5, Kt = ln21.6/5, t = ln4.3/.0069 =210 ()