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If AB is an isothermal BC is an isochor...

If AB is an isothermal BC is an isochoric and AC is an adiabatic, which of the graphs correctly represents given in figure.

A

B

C

D

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the characteristics of the different thermodynamic processes mentioned: isothermal, isochoric, and adiabatic. Let's break down the solution step by step. ### Step 1: Understand the Processes 1. **Isothermal Process (AB)**: This process occurs at a constant temperature. For an ideal gas, the relationship between pressure (P) and volume (V) is given by \( PV = nRT \). The graph of an isothermal process is a hyperbola in the PV diagram, and it has a gentle slope. 2. **Isochoric Process (BC)**: This process occurs at a constant volume. In a PV diagram, this is represented as a vertical line since the volume does not change, and pressure can vary with temperature. 3. **Adiabatic Process (AC)**: This process occurs without heat exchange with the surroundings. For an ideal gas, the relationship is given by \( PV^\gamma = \text{constant} \), where \( \gamma \) is the heat capacity ratio. The slope of an adiabatic process is steeper than that of an isothermal process in the PV diagram. ### Step 2: Analyze the Graphs - **Graph AB (Isothermal)**: Should be a hyperbolic curve that slopes gently downwards. - **Graph BC (Isochoric)**: Should be a vertical line since volume is constant. - **Graph AC (Adiabatic)**: Should be a curve that slopes downwards but is steeper than the isothermal curve. ### Step 3: Compare the Slopes - The slope of the adiabatic process (AC) is steeper than that of the isothermal process (AB). - The isochoric process (BC) is a vertical line, indicating no change in volume. ### Step 4: Identify the Correct Graph From the analysis, we can conclude that the correct graph must show: - A gentle downward slope for AB (isothermal). - A vertical line for BC (isochoric). - A steeper downward slope for AC (adiabatic). After comparing the options provided in the figures, we find that **Graph B** correctly represents these characteristics. ### Final Answer The correct graph that represents the processes is **Graph B**. ---
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