For the Carnot cycle of an ideal gas, the following are schematic diagrams of the cycle in non-$p-V$ coordinate graphs. Identify which of these are correct and select the option that includes **all** correct diagrams.  

1. <MultiModal>![This image is a two-dimensional line graph with two perpendicular axes, the vertical axis labeled T and the horizontal axis labeled p. The axes do not display specific numerical ranges or units. The graph shows a closed quadrilateral with four bold vertices. The left and right sides are curves, with the right curve being flatter than the left. The top and bottom sides are straight lines, with the top line longer than the bottom. Starting from the bottom-left corner, there is a right-upward convex curve, followed by a horizontal rightward line, then a left-downward convex curve, and finally a horizontal leftward line returning to the starting point. The vertices are not marked with explicit numbers or symbols. There is no title, legend, or additional text, numbers, symbols, or chemical formulas.](/media/uploads/f135cc86-41d1-4ffd-b2f8-6468ce466065.png)</MultiModal>  

2. <MultiModal>![This image is a two-dimensional line graph with two perpendicular axes, the vertical axis labeled S and the horizontal axis labeled V. The axes do not display specific numerical ranges or units. The graph shows a closed quadrilateral with four bold vertices. The left and right sides are curves, with the right curve being flatter than the left. The top and bottom sides are straight lines, with the top line longer than the bottom. Starting from the bottom-left corner, there is a right-upward convex curve, followed by a horizontal rightward line, then a left-downward convex curve, and finally a horizontal leftward line returning to the starting point. The vertices are not marked with explicit numbers or symbols. There is no title, legend, or additional text, numbers, symbols, or chemical formulas.](/media/uploads/11a22f7d-b4fd-4b94-ae85-3dc7bd5b5b87.png)</MultiModal>  

3. <MultiModal>![This image is a two-dimensional line graph with two perpendicular axes, the vertical axis labeled H and the horizontal axis labeled T. The axes do not display specific numerical ranges or units. The graph shows a line segment extending from the bottom-left to the top-right, with both endpoints bold. The endpoints and the origin of the axes are nearly colinear. There is no title, legend, or additional text, numbers, symbols, or chemical formulas.](/media/uploads/a2792869-2bf3-4955-9575-8d04fb32ee41.png)</MultiModal>  

4. <MultiModal>![This image is a two-dimensional line graph with two perpendicular axes, the vertical axis labeled T and the horizontal axis labeled V. The axes do not display specific numerical ranges or units. The graph shows a closed quadrilateral with four bold vertices. The left and right sides are curves, with the right curve being flatter than the left. The top and bottom sides are straight lines, with the top line shorter than the bottom. Starting from the top-left corner, there is a right-downward convex curve, followed by a horizontal rightward line, then a left-upward convex curve, and finally a horizontal leftward line returning to the starting point. The vertices are not marked with explicit numbers or symbols. There is no title, legend, or additional text, numbers, symbols, or chemical formulas.](/media/uploads/5a569752-85f1-4f44-8449-2f7841a5dc31.png)</MultiModal>
对于理想气体的卡诺循环，以下为该循环在非 $p-V$ 坐标图中的示意图，其中哪些是正确的，选出包含**所有**正确示意图的选项？

1.<MultiModal>![该图像是一个二维线图，图中有两条互相垂直的坐标轴，竖直轴标记为 T，水平轴标记为 p。坐标轴上没有显示具体的数值范围或单位。图中有一个闭合的四边形，四个顶点加粗；其左侧和右侧的边为曲线，右侧曲线比左侧更平缓；顶部和底部的边为直线，顶边比底边更长。从左下角开始，先是一条向右向上倾斜且下凸的边，然后是一条水平向右的边，接着是一条向左向下倾斜且下凸的边，最后是一条水平向左的边，回到起点。四边形的顶点处没有明确的数字或符号标记。没有标题、图例，也没有额外的文字、数字、符号或化学式。](/media/uploads/f135cc86-41d1-4ffd-b2f8-6468ce466065.png)</MultiModal>

2.<MultiModal>![该图像是一个二维线图，图中有两条互相垂直的坐标轴，竖直轴标记为 S，水平轴标记为 V。坐标轴上没有显示具体的数值范围或单位。图中有一个闭合的四边形，四个顶点加粗；其左侧和右侧的边为曲线，右侧曲线比左侧更平缓；顶部和底部的边为直线，顶边比底边更长。从左下角开始，先是一条向右向上倾斜且下凸的边，然后是一条水平向右的边，接着是一条向左向下倾斜且下凸的边，最后是一条水平向左的边，回到起点。四边形的顶点处没有明确的数字或符号标记。没有标题、图例，也没有额外的文字、数字、符号或化学式。](/media/uploads/11a22f7d-b4fd-4b94-ae85-3dc7bd5b5b87.png)</MultiModal>

3.<MultiModal>![该图像是一个二维线图，图中有两条互相垂直的坐标轴，竖直轴标记为 H，水平轴标记为 T。坐标轴上没有显示具体的数值范围或单位。图中有一条从左下一点延伸至右上一点的线段，两端点加粗；线段的两端点和坐标轴原点接近共直线。没有标题、图例，也没有额外的文字、数字、符号或化学式。](/media/uploads/a2792869-2bf3-4955-9575-8d04fb32ee41.png)</MultiModal>

4.<MultiModal>![该图像是一个二维线图，图中有两条互相垂直的坐标轴，竖直轴标记为 T，水平轴标记为 V。坐标轴上没有显示具体的数值范围或单位。图中有一个闭合的四边形，四个顶点加粗；其左侧和右侧的边为曲线，右侧曲线比左侧更平缓；顶部和底部的边为直线，顶边比底边更短。从左上角开始，先是一条向右向下倾斜且下凸的边，然后是一条水平向右的边，接着是一条向左向上倾斜且下凸的边，最后是一条水平向左的边，回到起点。四边形的顶点处没有明确的数字或符号标记。没有标题、图例，也没有额外的文字、数字、符号或化学式。](/media/uploads/5a569752-85f1-4f44-8449-2f7841a5dc31.png)</MultiModal>
1,2,3
1,3,4
1,2
2,3
3,4
2,4
1,4
None of the above options are correct
1,2,3
1,3,4
1,2
2,3
3,4
2,4
1,4
以上选项均不对
The Carnot cycle consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

<Checkpoint>[The Carnot cycle consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression](0.5)</Checkpoint>

Examining the $T-p$ diagram: the two isothermal processes correspond to horizontal lines, while the adiabatic process follows $p^{1-\gamma}T^\gamma=C$, which can be rewritten as $T=C' p^\frac{\gamma-1}{\gamma}$. Here, $\frac{\gamma-1}{\gamma}<1$, so the adiabatic segment of the $T-p$ curve should be convex upward, not convex downward as shown in the diagram. Thus, Figure 1 is incorrect.

<Checkpoint>[$T=C' p^\frac{\gamma-1}{\gamma}$](0.5)</Checkpoint>

<Checkpoint>[The adiabatic process's $T-p$ curve should be convex upward; Figure 1 is incorrect](1)</Checkpoint>

Examining the $S-V$ diagram: the two adiabatic processes have $Q=0$, so $S=0$, corresponding to horizontal lines. For the isothermal process, $\Delta S=nR\cdot ln\frac{V_2}{V_1}$, meaning the expression for $S$ contains a logarithmic term in $V$, resulting in a convex upward function. However, the diagram shows a convex downward curve, so Figure 2 is incorrect.

<Checkpoint>[$\Delta S=nR\cdot ln\frac{V_2}{V_1}$](0.5)</Checkpoint>

<Checkpoint>[The isothermal process's $S-V$ curve should be convex upward; Figure 2 is incorrect](1)</Checkpoint>

Examining the $H-T$ diagram: For an ideal gas, the isothermal process has $H=0$. Therefore, the Carnot cycle on the $H-T$ diagram consists of only two state points. Since $\Delta H/\Delta T=C_p$, the line connecting these two points is straight, which is correct. Additionally, it is necessary to verify whether this line passes through the origin, as for an ideal gas, $H\rightarrow 0$ when $T\rightarrow 0$. The schematic satisfies this condition as well. In summary, Figure 3 is correct.

<Checkpoint>[The Carnot cycle on the $H-T$ diagram consists of only two state points](0.5)</Checkpoint>

<Checkpoint>[The line connecting the two state points is straight](0.5)</Checkpoint>

<Checkpoint>[The $H-T$ curve's extension passes through the origin of the coordinate axes](0.5)</Checkpoint>

Examining the $T-V$ diagram: the two isothermal processes correspond to horizontal lines, while the adiabatic process follows $TV^{\gamma-1}=C$, so $T=CV^{1-\gamma}$, which is a convex downward function. For the same temperature, $\Delta V=V_2-V_1=(\frac{C_2}{T})^{\frac{1}{\gamma-1}}-(\frac{C_1}{T})^{\frac{1}{\gamma-1}}=C'(\frac{1}{T})^\frac{1}{\gamma-1}$. For $T_2>T_1$, $\Delta V_2<\Delta V_1$, meaning the top edge of the graph is shorter than the bottom edge. In summary, Figure 4 is correct.

<Checkpoint>[$T=CV^{1-\gamma}$](0.5)</Checkpoint>

<Checkpoint>[The isothermal process's $T-V$ curve is convex downward](0.5)</Checkpoint>

<Checkpoint>[The top edge of the $T-V$ curve is shorter than the bottom edge](0.5)</Checkpoint>

Therefore, the answer is option E.
卡诺循环由四个可逆过程组成：等温膨胀、绝热膨胀、等温压缩、绝热压缩。

<Checkpoint>[卡诺循环由四个可逆过程组成：等温膨胀、绝热膨胀、等温压缩、绝热压缩](0.5)</Checkpoint>

看 $T-p$ 图：两段等温过程对应水平线，而绝热过程有$p^{1-\gamma}T^\gamma=C$，变形得$T=C' p^\frac{\gamma-1}{\gamma}$，其中$\frac{\gamma-1}{\gamma}<1$，故绝热一段的 $T-p$ 图线应是上凸的，并非图中的下凸，图1错误。

<Checkpoint>[$T=C' p^\frac{\gamma-1}{\gamma}$](0.5)</Checkpoint>

<Checkpoint>[绝热过程的 $T-p$ 图线应是上凸的，图1错误](1)</Checkpoint>

看 $S-V$ 图：两段绝热过程$Q=0$，故$S=0$，对应水平线。而等温过程有$\Delta S=nR\cdot ln\frac{V_2}{V_1}$，故$S$表达式中含$V$的项为对数项，为上凸函数，并非图中的下凸，图2错误。

<Checkpoint>[$\Delta S=nR\cdot ln\frac{V_2}{V_1}$](0.5)</Checkpoint>

<Checkpoint>[等温过程的 $S-V$ 图线应是上凸的，图2错误](1)</Checkpoint>


看 $H-T$ 图：对于理想气体，等温过程$H=0$。所以卡诺循环在 $H-T$ 图上只有两个状态点。$\Delta H/\Delta T=C_p$，两状态点连线为直线，正确。此外，还需检查该直线是否过原点，因为理想气体$T\rightarrow 0$时$H\rightarrow 0$，示意图在这一要素上也是对的。综上，图3正确。

<Checkpoint>[卡诺循环在 $H-T$ 图上只有两个状态点](0.5)</Checkpoint>

<Checkpoint>[两状态点连线为直线](0.5)</Checkpoint>

<Checkpoint>[$H-T$图线延长线过坐标轴原点](0.5)</Checkpoint>

看 $T-V$ 图：两段等温过程对应水平线，而绝热过程有$TV^{\gamma-1}=C$，故$T=CV^{1-\gamma}$，为下凸函数。而同一温度的$\Delta V=V_2-V_1=(\frac{C_2}{T})^{\frac{1}{\gamma-1}}-(\frac{C_1}{T})^{\frac{1}{\gamma-1}}=C'(\frac{1}{T})^\frac{1}{\gamma-1}$。对于$T_2>T_1$，有$\Delta V_2<\Delta V_1$，所以图形的顶边短于底边。综上，图4正确。

<Checkpoint>[$T=CV^{1-\gamma}$](0.5)</Checkpoint>

<Checkpoint>[等温过程的 $T-V$ 图线是下凸的](0.5)</Checkpoint>

<Checkpoint>[$T-V$ 图线的顶边短于底边](0.5)</Checkpoint>

所以答案是选项E。