Question

The ideal gas equation for an adiabatic process is:
A. $P{V^\gamma } = {\text{constant}}$
B. $T{V^{\gamma + 1}} = {\text{constant}}$
C. $P\left( {\gamma - 1} \right)T = {\text{constant}}$
D. $P\left( {\gamma + 1} \right)T = {\text{constant}}$

Answer 1

Hint:The ideal gas law is the equation of the state of a hypothetical ideal gas, sometimes called the general gas equation. In many conditions, it is a reasonable approximation of the behaviour of several gases, but it has many drawbacks.
The ideal gas equation is written as:
$PV = nRT$
Where $P$, $V$ and $T$ are the pressure, volume and temperature; $n$ is the amount of substance and $R$ is the ideal gas constant.

Complete answer:
In thermodynamics, an adiabatic process is a type of thermodynamic process that happens between the system and its surroundings without transmitting heat or mass. Unlike an isothermal process, an adiabatic process only transmits energy as work to the environment. The principle used to describe the first law of thermodynamics still follows it conceptually and is therefore a core thermodynamic concept.
A mechanism without heat or matter transfer to or from a system is called adiabatic, such that $Q = 0$, and it is said that such a system is adiabatically isolated. The statement that a method is adiabatic is a hypothesis sometimes made to simplify. For instance, the compression of a gas inside an engine cylinder is believed to occur so quickly that none of the energy of the device can be transmitted out as heat to the atmosphere on the time scale of the compression process.
The polytropic process equation can represent the mathematical equation for an ideal gas undergoing a reversible (i.e., no entropy generation) adiabatic process which is given as:
$P{V^\gamma } = \,{\text{constant}}$

Hence, option A is correct.

Note:We should not be confused between the adiabatic or isothermal or isobaric process. In adiabatic processes the heat remains constant. It is neither added nor removed from the process.In isothermal processes temperature remains constant and in isobaric processes the pressure remains constant.