- #1

tracker890 Source h

- 90

- 11

- Homework Statement
- Puzzled by why it's a reversible adiabatic process but not isentropic.

- Relevant Equations
- Wb,rev equation

Q1: Why can't set ##Q_{in,net}=0## and use equation (2) to obtain ##W_{act,in}=\left( \bigtriangleup U \right) _{cv}##?

Q2: If assume it's a reversible process, why can't equation (3) determine (△S)sys=0?

ref1.

ref2.

$$

W_{rev,in}=W_{act,in}-W_{surr}=W_{act,in}+P_0\left( V_2-V_1 \right) \cdots \text{(1)}

$$

$$

\ \ Q_{in,net}+W_{act,in}=\left( \bigtriangleup U \right) _{cv}\cdots \text{(2)}

$$

$$

\ \ T_0\left( \bigtriangleup S \right) _{sys}=\sum{\left( \frac{T_0}{T_k} \right)}Q_k\cdots \text{(3)}

$$

$$

\ let\ \ Q_{in,net}=Q_k

$$

$$

\left( 2 \right) +\left( 3 \right) :\

$$

$$

\ \ W_{act,in}=\sum{\left( -1+\frac{T_0}{T_k} \right)}\cancel{Q_k}+\left( \bigtriangleup U \right) _{cv}-\ T_0\left( \bigtriangleup S \right) _{sys}

$$

$$

\ \ \ \ \ \ \ \ =\left( U_2-U_1 \right) -T_0\left( S_2-S_1 \right) _{sys}\cdots \text{(4)}

$$

$$

Substitute\left( 4 \right) into\left( 1 \right)

$$

$$

W_{rev,in}=\left( U_2-U_1 \right) -T_0\left( S_2-S_1 \right) _{sys}+P_0\left( V_2-V_1 \right)

$$

$$

=m\left[ \left( u_2-u_1 \right) -T_0\left( s_2-s_1 \right) _{sys}+P_0\left( v_2-v_1 \right) \right]

$$

$$

=-m\left[ \left( u_1-u_2 \right) -T_0\left( s_1-s_2 \right) _{sys}+P_0\left( v_1-v_2 \right) \right] \cdots \text{(5)}

$$

Q2: If assume it's a reversible process, why can't equation (3) determine (△S)sys=0?

ref1.

ref2.

$$

W_{rev,in}=W_{act,in}-W_{surr}=W_{act,in}+P_0\left( V_2-V_1 \right) \cdots \text{(1)}

$$

$$

\ \ Q_{in,net}+W_{act,in}=\left( \bigtriangleup U \right) _{cv}\cdots \text{(2)}

$$

$$

\ \ T_0\left( \bigtriangleup S \right) _{sys}=\sum{\left( \frac{T_0}{T_k} \right)}Q_k\cdots \text{(3)}

$$

$$

\ let\ \ Q_{in,net}=Q_k

$$

$$

\left( 2 \right) +\left( 3 \right) :\

$$

$$

\ \ W_{act,in}=\sum{\left( -1+\frac{T_0}{T_k} \right)}\cancel{Q_k}+\left( \bigtriangleup U \right) _{cv}-\ T_0\left( \bigtriangleup S \right) _{sys}

$$

$$

\ \ \ \ \ \ \ \ =\left( U_2-U_1 \right) -T_0\left( S_2-S_1 \right) _{sys}\cdots \text{(4)}

$$

$$

Substitute\left( 4 \right) into\left( 1 \right)

$$

$$

W_{rev,in}=\left( U_2-U_1 \right) -T_0\left( S_2-S_1 \right) _{sys}+P_0\left( V_2-V_1 \right)

$$

$$

=m\left[ \left( u_2-u_1 \right) -T_0\left( s_2-s_1 \right) _{sys}+P_0\left( v_2-v_1 \right) \right]

$$

$$

=-m\left[ \left( u_1-u_2 \right) -T_0\left( s_1-s_2 \right) _{sys}+P_0\left( v_1-v_2 \right) \right] \cdots \text{(5)}

$$