A)
Interpretation:
To determine the coefficient of thermal expansion and isothermal compressibility for the given condition
Concept introduction:
Coefficient of thermal expansion:
The change in length of an object with unit degree increase in temperature at constant pressure is known as coefficient of thermal expansion.
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
Isothermal compressibility:
Isothermal compressibility is the reciprocal of the bulb modulus.
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
A)
Explanation of Solution
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
The equation (1) can be rewritten as:
Here, given value of molar volume is
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
The equation (3) can be rewritten as:
Here, final pressure is
Take initial and final temperature as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given value of molar volume
Substitute
The coefficient of thermal expansion
Take the initial and final pressure as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given value of molar volume
Substitute
The isothermal compressibility
B)
Interpretation:
To determine the coefficient of thermal expansion and isothermal compressibility for the given condition
Concept introduction:
Coefficient of thermal expansion:
The change in length of an object with unit degree increase in temperature at constant pressure is known as coefficient of thermal expansion.
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
Isothermal compressibility:
Isothermal compressibility is the reciprocal of the bulb modulus.
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
B)
Explanation of Solution
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
The equation (1) can be rewritten as:
Here, given value of molar volume is
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
The equation (3) can be rewritten as:
Here, final pressure is
Take initial and final temperature as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given value of molar volume
Substitute
The coefficient of thermal expansion
Take the initial and final pressure as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given value of molar volume
Substitute
The isothermal compressibility
C)
Interpretation:
To determine the coefficient of thermal expansion and isothermal compressibility for the given condition
Concept introduction:
Coefficient of thermal expansion:
The change in length of an object with unit degree increase in temperature at constant pressure is known as coefficient of thermal expansion.
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
Isothermal compressibility:
Isothermal compressibility is the reciprocal of the bulb modulus.
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
C)
Explanation of Solution
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
The equation (1) can be rewritten as:
Here, given value of molar volume is
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
The equation (3) can be rewritten as:
Here, final pressure is
Take initial and final temperature as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given value of molar volume
Substitute
The coefficient of thermal expansion
Take the initial and final pressure as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, write the value of given value of molar volume corresponding to given pressure of
Substitute
The isothermal compressibility
D)
Interpretation:
To determine the coefficient of thermal expansion and isothermal compressibility for the given condition
Concept introduction:
Coefficient of thermal expansion:
The change in length of an object with unit degree increase in temperature at constant pressure is known as coefficient of thermal expansion.
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
Isothermal compressibility:
Isothermal compressibility is the reciprocal of the bulb modulus.
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
D)
Explanation of Solution
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
The equation (1) can be rewritten as:
Here, given value of molar volume is
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
The equation (3) can be rewritten as:
Here, final pressure is
Take initial and final temperature as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given molar volume
Substitute
Hence, the coefficient of thermal expansion
Take the initial and final pressure as
Referring to appendix Table A-4, “compressed liquid”, the value of initial molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of final molar volume
Referring to appendix Table A-4, “compressed liquid”, the value of given value of molar volume
Substitute
Hence, the isothermal compressibility
E)
Interpretation:
To comment on the validity to model isothermal compressibility and coefficient of thermal expansion as constants for liquids at high pressure.
Concept introduction:
Coefficient of thermal expansion:
The change in length of an object with unit degree increase in temperature at constant pressure is known as coefficient of thermal expansion.
The formula to calculate the coefficient of thermal expansion
Here, molar volume is
Isothermal compressibility:
Isothermal compressibility is the reciprocal of the bulb modulus.
The formula to calculate the isothermal compressibility
Here, change in molar volume and change in pressure at constant temperature is
E)
Explanation of Solution
Similar to the approximation of heat capacity to a constant, the approximation of isothermal compressibility and coefficient of thermal expansion as a constant is very suited for some instance specifically when the intervals of pressure and/or temperature are small. However from this problem, it can be noted that the variation in both isothermal compressibility and coefficient of thermal expansion are very substantial over higher intervals of temperature and pressure. It can also be noticed that both isothermal compressibility and coefficient of thermal expansion are functions of both temperature and pressure.
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