Which of following statements (s) is true
I -Slope of isotherm at critical point is maximum.
II-Larger is the value of `T_(c)` easler is the liquification of gas.
III-Vander waals equation of state is applicable below critical temperature at all pressure.
Which of following statements (s) is true
I -Slope of isotherm at critical point is maximum.
II-Larger is the value of `T_(c)` easler is the liquification of gas.
III-Vander waals equation of state is applicable below critical temperature at all pressure.
I -Slope of isotherm at critical point is maximum.
II-Larger is the value of `T_(c)` easler is the liquification of gas.
III-Vander waals equation of state is applicable below critical temperature at all pressure.
A
only I
B
I & II
C
II & III
D
only II
Text Solution
AI Generated Solution
The correct Answer is:
To determine which of the statements regarding the gaseous state is true, we will analyze each statement one by one.
### Step 1: Evaluate Statement I
**Statement I:** "Slope of isotherm at critical point is maximum."
- The slope of the isotherm represents how pressure changes with volume at a constant temperature. At the critical point, the isotherm does not have a defined slope because it transitions from gas to liquid without a distinct phase change. Therefore, the slope at the critical point is zero, not maximum.
- **Conclusion:** This statement is **false**.
### Step 2: Evaluate Statement II
**Statement II:** "Larger is the value of T_c, easier is the liquefaction of gas."
- The critical temperature (T_c) is the temperature above which a gas cannot be liquefied, regardless of the pressure applied. A higher T_c means that the gas can be liquefied at higher temperatures, which implies that less cooling is required to liquefy the gas.
- Therefore, if T_c is larger, it indeed becomes easier to liquefy the gas.
- **Conclusion:** This statement is **true**.
### Step 3: Evaluate Statement III
**Statement III:** "Van der Waals equation of state is applicable below critical temperature at all pressure."
- The Van der Waals equation is a modification of the ideal gas law that accounts for intermolecular forces and the volume occupied by gas molecules. While it is applicable below the critical temperature, it is not valid at all pressures. At very high pressures, gases may behave non-ideally, and the Van der Waals equation may not accurately describe the behavior of the gas.
- **Conclusion:** This statement is **false**.
### Final Conclusion
- The true statements are: **Only Statement II is true.**
To determine which of the statements regarding the gaseous state is true, we will analyze each statement one by one.
### Step 1: Evaluate Statement I
**Statement I:** "Slope of isotherm at critical point is maximum."
- The slope of the isotherm represents how pressure changes with volume at a constant temperature. At the critical point, the isotherm does not have a defined slope because it transitions from gas to liquid without a distinct phase change. Therefore, the slope at the critical point is zero, not maximum.
- **Conclusion:** This statement is **false**.
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Which of the following statement (s) is true I- Slpe of isotherm at critical point is maximum II - Larger is the value of T_(C) easier is the liquification of gas. III- Vander walls equation of state is applicable below critical temperature at all pressure.
Which of the following statement (s) is true I- Slpe of isotherm at critical point is maximum II - Larger is the value of T_(C) easier is the liquification of gas. III- Vander walls equation of state is applicable below critical temperature at all pressure.
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The essential conditions for liquefaction of gases were discovered by Andrews in 1869 as a result of his study of pressure-volume-temperature relationship for CO_(2) . If was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature (T_(c)) . The pressure required to liquefy a gas at this temperature is called the critical pressure (P_(c)) . The volume occupied by one mole of the substance at the critical temperature and pressure is called critcal volume. Critical constants are related with van der Waals' constant as follows: V_(c) = 3b, P_(c) = (a)/(27b^(2)), T_(c) = (8a)/(27 Rb) Which of the following parameters is three times the van der Waals' constant 'b' ?
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