I teach undergraduate thermodynamics and I was quite ashamed that I couldn't explain to a student, the following. I thought I'd bring it to physics.SE in hope of providing my student a good explanation.
The question was concerning the energy equation for an open system:
$$ \underbrace{\frac{\mathrm{d} E}{\mathrm{d}t}}_{\begin{array}{c}\text{Rate of change}\\ \text{of total energy}\\ \text{in the system}\end{array}} = \underbrace{\delta \dot{Q}}_{\begin{array}{c}\text{Rate of}\\ \text{heat transfer}\end{array}} - \underbrace{\delta \dot{W}}_{\begin{array}{c}\text{Work}\\ \text{extracted/input}\end{array}} + \underbrace{\dot{m} \left(h_1 + \frac{V_1^2}{2} + g z_1 \right)}_\text{energy of inlet stream} - \underbrace{\dot{m} \left(h_1 + \frac{V_1^2}{2} + g z_1 \right)}_\text{energy of outlet stream}$$
The young lady asked me that for steady state operations, the rate of change of total energy, $dE/dt$ is zero. So why are $\delta \dot{Q}$ and $\delta \dot{W}$ are not zero as they are also rates of heat exchange and work generation/input. It is just obvious to me but I don't know how to explain this to a 17 year old.
I'd appreciate it if someone could help me out on this.
:(
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