# Thermodynamics Questions and Answers – Law of Corresponding States

This set of Thermodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Law of Corresponding States”.

1. For a gas, the compressibility factor Z depends on
a) pressure and volume
b) pressure and temperature
c) volume and temperature
d) pressure, volume and temperature

Explanation: For a particular gas, Z depends on pressure and temperature.

2. We can use Z instead of directly plotting v.
a) true
b) false

Explanation: The main advantage of using Z instead of v is a smaller range of values in plotting.

3. How could we use one compressibility factor chart for all the substances?
a) it would be more convenient
b) the general shapes of the vapour dome and of the constant temperature lines on the p-v plane can be similar for all substances
c) their similarity can be exploited using dimensionless properties
d) all of the mentioned

Explanation: These dimensionless properties called reduced properties can be used for all the substances.

4. Which of the following property is used as the dimensionless property?
a) reduced pressure
b) reduced volume
c) reduced temperature
d) all of the mentioned

Explanation: The reduced pressure is the ratio of existing pressure to the critical pressure of the substance and like this all other properties are written.

5. Which of the following statement is true?
a) the specific volumes of different gases at same pressure and temperature are different
b) the reduced volumes of different gases at same reduced pressure and reduced temperature are same
c) both of the mentioned
d) none of the mentioned

Explanation: This is found from the experimental data and because of this reduced properties are used.
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6. Value of critical compressibility factor Zc is taken to be constant.
a) true
b) false

Explanation: The experimental values of Zc fall within a narrow range of 0.20-0.30, hence it is taken constant.

7. The generalized compressibility chart is a plot in
a) when reduced pressure is plotted as a function of reduced temperature and Z
b) when reduced temperature is plotted as a function of reduced pressure and Z
c) when Z is plotted as a function of reduced pressure and reduced temperature
d) none of the mentioned

Explanation: The generalized compressibility chart is found to be satisfactory for a great variety of substances.

8. The law of corresponding states is a relation among
a) reduced pressure and reduced temperature
b) reduced volume and reduced temperature
c) reduced volume and reduced pressure
d) reduced pressure and reduced temperature and reduced volume

Explanation: This relation can be derived from the equations of state.

9. The corrected gas equation is a cubic in v, which of the following statement is true about its roots?
a) at low temperature, three positive real roots exists
b) at critical temperature, the three real roots become equal
c) at high temperature, only one real root exists
d) all of the mentioned

Explanation: The equation has three roots which are different for different temperature and pressure.

10. The value of compressibility factor at the critical state for a van der Waals gas is
a) 0.325
b) 0.350
c) 0.375
d) 0.400

Explanation: This value comes from the relation, R=(8/3)(p*v/T) where p,v,T are critical values.

11. At very low pressures Z approaches
a) zero
b) unity
c) 0.50
d) infinity

Explanation: At very low pressures, a real gas approaches the ideal gas behaviour.

12. Which of the following statement is true about the reduced equation of state?
a) the individual coefficients a,b,R for a particular gas have disappeared
b) it reduces the properties of all gases to one formula
c) it tells us that to what extent a real gas obeys van der Waals equation
d) all of the mentioned

Explanation: These are the properties of the reduced equation of state.

13. The Boyle temperature is given by
a) a/(b*R)
b) b/(a*R)
c) R/(a*b)
d) 1/(a*b*R)

Explanation: It is obtained when the value of B=b-a/(RT) is zero, i.e., B=0.

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