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The Clausius-Clapeyron equation gives the slope of curve on
- a)P - V plot
- b)P - h plot
- c)P - T plot
- d)T - s plot
Correct answer is option 'C'. Can you explain this answer?
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The Clausius-Clapeyron equation gives the slope of curve ona)P - V plo...
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Clausius-Clapeyron Equation in P-T Plot:
The Clausius-Clapeyron equation is a fundamental equation in thermodynamics that relates the vapor pressure of a substance to its temperature. It provides a mathematical relationship that describes the behavior of the phase equilibrium curve between the liquid and vapor phases of a substance.
The equation is expressed as:
ln(P2/P1) = (ΔHvap/R)(1/T1 - 1/T2)
where P1 and P2 are the vapor pressures of the substance at temperatures T1 and T2 respectively, ΔHvap is the enthalpy of vaporization, R is the gas constant, and T1 and T2 are the temperatures in Kelvin.
The Clausius-Clapeyron equation is particularly useful when representing the phase equilibrium curve on a P-T plot. In this plot, the pressure (P) is plotted on the y-axis, and the temperature (T) is plotted on the x-axis.
Explanation:
The correct answer is option 'C' because the Clausius-Clapeyron equation gives the slope of the curve on a P-T plot. Let's understand why:
1. P-T plot:
- The P-T plot is a graph that represents the behavior of a substance as it undergoes a phase change from a liquid to a vapor.
- The pressure (P) is plotted on the y-axis, and the temperature (T) is plotted on the x-axis.
- The phase equilibrium curve on the P-T plot represents the conditions at which the substance exists in equilibrium between the liquid and vapor phases.
2. Clausius-Clapeyron equation:
- The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature.
- It provides a mathematical relationship that describes the behavior of the phase equilibrium curve.
- The equation gives the slope of the curve on the P-T plot, representing how the vapor pressure changes with temperature.
3. Slope interpretation:
- The slope of a curve represents the rate at which one variable changes with respect to another variable.
- In the context of the Clausius-Clapeyron equation, the slope represents the rate at which the vapor pressure changes with temperature.
- A steeper slope indicates a higher rate of change in vapor pressure with temperature, while a shallower slope indicates a lower rate of change.
Therefore, the Clausius-Clapeyron equation is used to determine the slope of the phase equilibrium curve on a P-T plot, making option 'C' the correct answer.
The Clausius-Clapeyron equation is a fundamental equation in thermodynamics that relates the vapor pressure of a substance to its temperature. It provides a mathematical relationship that describes the behavior of the phase equilibrium curve between the liquid and vapor phases of a substance.
The equation is expressed as:
ln(P2/P1) = (ΔHvap/R)(1/T1 - 1/T2)
where P1 and P2 are the vapor pressures of the substance at temperatures T1 and T2 respectively, ΔHvap is the enthalpy of vaporization, R is the gas constant, and T1 and T2 are the temperatures in Kelvin.
The Clausius-Clapeyron equation is particularly useful when representing the phase equilibrium curve on a P-T plot. In this plot, the pressure (P) is plotted on the y-axis, and the temperature (T) is plotted on the x-axis.
Explanation:
The correct answer is option 'C' because the Clausius-Clapeyron equation gives the slope of the curve on a P-T plot. Let's understand why:
1. P-T plot:
- The P-T plot is a graph that represents the behavior of a substance as it undergoes a phase change from a liquid to a vapor.
- The pressure (P) is plotted on the y-axis, and the temperature (T) is plotted on the x-axis.
- The phase equilibrium curve on the P-T plot represents the conditions at which the substance exists in equilibrium between the liquid and vapor phases.
2. Clausius-Clapeyron equation:
- The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature.
- It provides a mathematical relationship that describes the behavior of the phase equilibrium curve.
- The equation gives the slope of the curve on the P-T plot, representing how the vapor pressure changes with temperature.
3. Slope interpretation:
- The slope of a curve represents the rate at which one variable changes with respect to another variable.
- In the context of the Clausius-Clapeyron equation, the slope represents the rate at which the vapor pressure changes with temperature.
- A steeper slope indicates a higher rate of change in vapor pressure with temperature, while a shallower slope indicates a lower rate of change.
Therefore, the Clausius-Clapeyron equation is used to determine the slope of the phase equilibrium curve on a P-T plot, making option 'C' the correct answer.
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