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- Homework Statement
- Establishing the Relationship Between Input Heat for Energy Conservation and Input Heat Defined by Entropy.

- Relevant Equations
- entropy balance equation.

entropy definition formula.

Q： What are the differences between the heat transfer calculated by the energy conservation equation and the heat transfer determined by the Gibbs relation? ##why\ \left( ans\_1 \right) \ne \left( ans\_2 \right) ##

reference

Energy balance：

$$

Q_{in,net}-W_{out,net}=\cancel{\bigtriangleup U_{cv}}\cdots \left( 1 \right)

$$

$$

Q_{in,net}=-Q

$$

$$

W_{out,net}=-W_{in}

$$

$$

\therefore \left( 1 \right) =-Q+W_{in}=0

$$

$$

\therefore Q=W_{in}=200KJ\cdots \cdots \left( ans\_1 \right)

$$

entropy balance equation.

entropy definition formula.

Gibbs relation.

$$

dS_{sys}=\left( \frac{\delta Q}{T_k} \right) _{int.rev}\cdots \left( 2 \right)

$$

$$

\bigtriangleup S_{sys}=m\left( \frac{\cancel{du}+p\cancel{dv}}{T_k} \right) =0

$$

$$

\therefore \left( 2 \right) =0

$$

$$

\therefore Q=0KJ\cdots \cdots \left( ans\_2 \right)

$$

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