Question

For a real gas, the compressibility factor Z has different values at different temperature and pressures. Which of the following is not correct under the given condition?
a. Z < 1 at very low pressure
b. Z > 1 at high pressure
c. Z = 1 under all conditions
d. Z = 1 at intermediate pressure

Answer 1

Hint: The compressibility factor (Z) is a useful thermodynamic property which is used in modifying the ideal gas law to account for the behaviour of real gases. In simpler terms it can also be defined as the modifying factor for real gases.

Complete step by step answer: The compressibility factor (Z) is also known as the compression factor or the gas deviation factor. It is known to be a correction factor which is used to describe the deviation of a real gas from the ideal gas behaviour. Mathematically, it can be defined as the ratio of actual volume at a given pressure and temperature to the ideal volume under the same temperature and pressure conditions. For a real gas, the compressibility factor (Z) has different values for different sets of temperature and pressure conditions. The compressibility factor can be written as:
$ Z\quad =\quad \cfrac { PV }{ nRT }$
where Z is the compressibility factor, P is the pressure, V is the volume, n is the no. of moles, R is the gas constant and T is the temperature.
For real gases, when the pressure is high, the value of Z will be greater than 1 i.e., Z > 1.
And when the pressure is very low, the value of Z will be less than 1 i.e., Z < 1.
And at intermediate pressures, the value of Z will be equal to 1 i.e., Z = 1.
Therefore, the options (a), (b), and (d) are true. Thus, the only false option is option (c). Hence it is the correct answer.

Note: Since, an ideal gas is a hypothetical gas whose molecules occupy negligible space and does not have any interactions. For ideal gases, the gas law, $PV = nRT$ holds true. So, in that case, the compressibility factor, Z = 1 at any pressure and temperature conditions.