A process on one mole of an ideal gas is defined as follow: (PA, VA, TA) ⟶(P=a, V=2 VA, T=T

step 1 Hello students in this question we have given the processes in which the initial states are P -A

A process on one mole of an ideal gas is defined as follow: ...

A process on one mole of an ideal gas is defined as follow: $$ \begin{aligned} \left(P_{A}, V_{A}, T_{A}\right) & \longrightarrow\left(P=a, V=2 V_{A}, T=T_{A}\right) \\ & \longrightarrow\left(P_{1}=P, V_{1}=2 V_{A}, T_{1}=b\right) \\ & \longrightarrow\left(P_{2}=P_{A}, V_{2}=V_{A}, T_{2}=c\right) \end{aligned} $$ The values of $a, b$, and $c$ are : (a) $\left(\frac{P_{A}}{2}, \frac{T_{A}}{2}, T_{A}\right)$ (b) $\left(P_{A}, T_{A}, T_{A}\right)$ (c) $\left(\frac{P_{A}}{4}, \frac{T_{A}}{4,} \frac{T_{A}}{3}\right)$ (d) none of these

A process on one mole of an ideal gas is defined as follow:
$$
\begin{aligned}
\left(P_{A}, V_{A}, T_{A}\right) & \longrightarrow\left(P=a, V=2 V_{A}, T=T_{A}\right) \\
& \longrightarrow\left(P_{1}=P, V_{1}=2 V_{A}, T_{1}=b\right) \\
& \longrightarrow\left(P_{2}=P_{A}, V_{2}=V_{A}, T_{2}=c\right)
\end{aligned}
$$
The values of $a, b$, and $c$ are :
(a) $\left(\frac{P_{A}}{2}, \frac{T_{A}}{2}, T_{A}\right)$
(b) $\left(P_{A}, T_{A}, T_{A}\right)$
(c) $\left(\frac{P_{A}}{4}, \frac{T_{A}}{4,} \frac{T_{A}}{3}\right)$
(d) none of these

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is fundamental in thermodynamics for relating pressure, volume, temperature, and the amount of gas. It provides the mathematical framework for predicting how state variables change during a process, making it indispensable for analyzing ideal gas behavior under different conditions.

Thermodynamic Processes

Thermodynamic processes involve changes in state variables like pressure, volume, and temperature. Understanding these processes is critical, as different paths (e.g., isothermal, isobaric) impose specific constraints that determine how one state variable changes in relation to another.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant. In such a process, the pressure and volume of an ideal gas are inversely related, a relationship that directly follows from the ideal gas law, facilitating the computation of unknown variables when the volume changes.

State Functions

State functions are properties that depend only on the current state of the system rather than on the path taken to reach that state. This concept is crucial in thermodynamics because it allows one to relate different states of a system directly, simplifying the analysis of multi-step processes.

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