Question

This graph expresses the various steps of the system containing 1 mole of gas. Which type of process system has when it moves from C to A?

A.Isochoric
B.Isobaric
C.Isothermal
D.Cyclic

Answer 1

To solve this question, it is required to have knowledge about the relation of pressure, temperature and volume of a gas, which can be concluded from the ideal gas equation, i.e. $PV = nRT$. We will substitute the values possible in this equation and remove the constant in order to get the relation between temperature, pressure and volume of the gas.
Formula Used:
$PV = nRT$ where P is for pressure of the gas, V is for volume of the gas, n is the number of moles, R is a constant ($8.314J{K^{ - 1}}mo{l^{ - 1}}$) and T is the temperature.

Complete step by step answer:
Since it is not given otherwise, we shall assume the gas to be ideal. As we already know that for an ideal gas at constant temperature, the change in pressure is always inversely proportional to the change in volume of the gas. In the question, it is already given that 1 mole of gas is present, so $n = 1$ and as R is a constant. The ideal gas equation can also be rewritten as:
$PV \propto T$ (Eq. 1)
From this relation, we can conclude that if any two of the quantities are variables, i.e. they change with respect to time, the third value will always be a constant.
For the process A to B, we can see directly from the graph that as the temperature is constant, the process is isothermal.
For the process B to C, we can see directly from the graph that as the volume remains constant it is an isochoric process.
For the process C to A, there is a change of both temperature (600K to 300K) and volume (20.0L to 10.0L). So, it is neither an isothermal nor an isochoric process. So, using Eq. 1 we know that since both volume and temperature are variables, the third quantity, i.e. the pressure of the gas must be constant. Thus, it is an isobaric process.

$\therefore$ The correct option is option C.

Note:
The relation between pressure and volume of a gas is also given by Boyle’s law. It states that pressure of a gas is always inversely proportional to its volume at constant temperature. The relation between volume and temperature is also given by Charles’s law. It states that volume of a gas is directly proportional to its temperature (in Kelvins) at constant pressure, which is the case in the process C to A.