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1. The problem statement, all variables and given/known data

The volume of the container in the attachment is given as V. The container is filled with a fluid whose heat capacity is C and whose viscosity decreases linearly with the temperature.

The fluid is initially at temperature T_{0}, and a pipe carries fluid at temperature T_{in}into it and at a rate which is equal to the rate of the volume lost from the container (i.e. its dV/dt). I am asked to find the time at which the temperature in the container will be T.

2. Relevant equations

3. The attempt at a solution

M/V = ρ

m(t) = ρVt/τ_{0}, where m(t) denotes the mass of water which passed through the pipe after time t.

dQ/dt = [ρV/τ_{0}]*C_{w}(T(t) - T_{c}) = ρVC_{w}dT/dt

Hence, dT/dt = (T_{c}- T(t))/T_{0}

Hence, T(t) = T_{c}+ (T_{H}- T_{c})e^{-t/τ0}= T_{in}+ (T_{0}- T_{in})e^{-t/τ0}

t = -τ_{0}ln((T - T_{in})/(T_{0}- T_{in}))

Is that correct?

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# Homework Help: Fluid's temperature change in time.

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