Question

LT.3. Use Laplace transforms to solve the single-tank mixing problem \frac{dT}{dt} = a (T_{in} - T) where $T(0) = T_0$ in each of the following cases: (a) $a = 2$, $T_0 = 0$ and $T_{in}(t) = 10H(t) + 10H(t - 3)$. (b) $a = 3$, $T_0 = 30$ and $T_{in}(t) = 10H(t) + 20H(t - 3) - 10H(t - 6)$. Here $H(t)$ is the Heaviside (or unit) step function. In each case, describe the temperature behaviour of the input and output flows.

          LT.3. Use Laplace transforms to solve the single-tank mixing problem
\frac{dT}{dt} = a (T_{in} - T) where $T(0) = T_0$
in each of the following cases:
(a) $a = 2$, $T_0 = 0$ and $T_{in}(t) = 10H(t) + 10H(t - 3)$.
(b) $a = 3$, $T_0 = 30$ and $T_{in}(t) = 10H(t) + 20H(t - 3) - 10H(t - 6)$.
Here $H(t)$ is the Heaviside (or unit) step function.
In each case, describe the temperature behaviour of the input and output flows.

LT.3. Use Laplace transforms to solve the single-tank mixing problem
(dT)/(dt) = a (Tin - T) where T(0) = T0
in each of the following cases:
(a) a = 2, T0 = 0 and Tin(t) = 10H(t) + 10H(t - 3).
(b) a = 3, T0 = 30 and Tin(t) = 10H(t) + 20H(t - 3) - 10H(t - 6).
Here H(t) is the Heaviside (or unit) step function.
In each case, describe the temperature behaviour of the input and output flows.

Added by Randy H.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Nishant Kumar

Step 1

Taking the Laplace transform of both sides of the equation, we get: sT(s) - T(0) = a(Tin(s) - T(s)) Since T(0) = To = 0, we can simplify the equation to: sT(s) = aTin(s) Substituting Tin(t) = 10H(t) + 10H(t-3), we have: sT(s) = 2(10H(s) + Show more…

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LT.3. Use Laplace transforms to solve the single-tank mixing problem dT = a(Tin - T) where T(0) = To dt in each of the following cases: (a) a = 2, To = 0 and Tin(t) = 10H(t) + 10H(t-3) (b) H0I - H0Z + H0I = Lpue08 = '8 = n(q) Here H(t) is the Heaviside (or unit) step function. In each case, describe the temperature behavior of the input and output flows.