0.2 moles of an ideal gas, is taken rouna the cvcle a b c as...

$0.2$ moles of an ideal gas, is taken rouna the cvcle $a b c$ as shown in the figure. The path $b-c$ is adiabaric , ness, $a-b$ is isovolumic process and $c-a$ is isobaric process. The temperature at ' $a$ ' and ' $b$ ' are $T_{a}=300 \mathrm{~K}$ and $\quad T_{b}=500 \mathrm{~K}$ and pressure at ' $a^{\prime}$ is 1 atmosphere. The volume at $' c^{\prime}$ is : (Given: $\gamma=\frac{C_{P}}{C_{V}}=\frac{5}{3}$, $R=8.205 \times 10^{-2}$ litre/atm/mol-K) (a) $6.9 \mathrm{~L}$ (b) $6.68 \mathrm{~L}$ (c) $5.52 \mathrm{~L}$ (d) $5.82 \mathrm{~L}$

$0.2$ moles of an ideal gas, is taken rouna the cvcle $a b c$ as shown in the figure. The path $b-c$ is adiabaric , ness, $a-b$ is isovolumic process and $c-a$ is isobaric process. The temperature at ' $a$ ' and ' $b$ ' are $T_{a}=300 \mathrm{~K}$ and $\quad T_{b}=500 \mathrm{~K}$
and pressure at ' $a^{\prime}$ is 1 atmosphere. The volume at $' c^{\prime}$ is :
(Given: $\gamma=\frac{C_{P}}{C_{V}}=\frac{5}{3}$, $R=8.205 \times 10^{-2}$ litre/atm/mol-K)
(a) $6.9 \mathrm{~L}$
(b) $6.68 \mathrm{~L}$
(c) $5.52 \mathrm{~L}$
(d) $5.82 \mathrm{~L}$

Key Concepts

Specific Heat Ratio (?)

The specific heat ratio, denoted by ? (gamma), is the ratio of the specific heat at constant pressure (C_P) to the specific heat at constant volume (C_V). It plays a critical role in characterizing adiabatic processes and influences the relationship between pressure, volume, and temperature during such processes. Its value affects how quickly temperature changes in response to changes in volume or pressure.

Isobaric Process

An isobaric process occurs at constant pressure. In an isobaric process, the volume of the gas changes directly with temperature changes, following the relation V/T = constant when combined with the Ideal Gas Law. This type of process is common in various thermodynamic applications where pressure is maintained constant.

Adiabatic Process

An adiabatic process is characterized by the absence of heat exchange between the system and its surroundings. In such a process, changes in the pressure, volume, and temperature of the gas occur solely due to work done by or on the system. The adiabatic condition is often described by equations like PV^? = constant or TV^(?-1) = constant, where ? is the specific heat ratio.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), and temperature (T) of an ideal gas with the amount of gas (n) and the universal gas constant (R). This law is used to calculate the state variables of a gas when it undergoes different processes and is essential for understanding gas behavior in various thermodynamic cycles.

Isovolumic (Isochoric) Process

An isovolumic (isochoric) process is one in which the volume of the system remains constant. Since the volume does not change, any heat added or removed from the system results solely in changes in the pressure and temperature following the relation P/T = constant. This process is fundamental in studying thermodynamic cycles where volume limitations are specified.

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