Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stop clock. A contains an ideal gas at standard temperature and pressure. $B$ is completely evacuated. The entire system is thermally insulated. The stop clock is suddenly opened. The process is:

Question

A real gas within a closed chamber at $ 27^\circ \text{C} $ undergoes the cyclic process as shown in the figure. The gas obeys the equation $ PV^3 = RT $ for the path A to B. The net work done in the complete cycle is (assuming $ R = 8 \, \text{J/molK} $):

Answer 1

The problem involves two cylinders, $A$ and $B$, which are initially of equal capacity and connected via a stop clock, with cylinder $A$ containing an ideal gas at standard temperature and pressure while cylinder $B$ is completely evacuated. The entire system is thermally insulated.

Upon opening the stop clock, the gas from cylinder $A$ will start expanding into cylinder $B$. Let's analyze this scenario based on the given options: isothermal, adiabatic, isochoric, and isobaric.

Isothermal Process: This process occurs when a system exchanges heat with its surroundings, maintaining a constant temperature throughout the expansion or compression of the gas. However, since the system described is thermally insulated, there is no heat exchange with the surroundings. Therefore, an isothermal process is not applicable.
Adiabatic Process: In an adiabatic process, there is no heat exchange, meaning $ q = 0 $. Since the system is thermally insulated (no heat enters or leaves the system), this is indeed an adiabatic process. The gas will expand freely and rapidly into the empty cylinder $B$.
Isochoric Process: An isochoric process involves a constant volume with no change in volume, often involving heat transfer resulting in changing pressure and temperature. Here, the volume is changing as the gas expands into the evacuated cylinder $B$. Thus, this process is not isochoric.
Isobaric Process: In an isobaric process, the pressure of the system remains constant as volume changes. As the gas expands into the evacuated cylinder $B$, the pressure will decrease in $A$ and increase in $B$, but it will not remain constant. Therefore, this is not an isobaric process.

From the above explanations, the correct option is the adiabatic process, ensuring no heat exchange occurs in this insulated system.

Answer 2

The problem involves two cylinders, $A$ and $B$, which are initially of equal capacity and connected via a stop clock, with cylinder $A$ containing an ideal gas at standard temperature and pressure while cylinder $B$ is completely evacuated. The entire system is thermally insulated.

Upon opening the stop clock, the gas from cylinder $A$ will start expanding into cylinder $B$. Let's analyze this scenario based on the given options: isothermal, adiabatic, isochoric, and isobaric.

Isothermal Process: This process occurs when a system exchanges heat with its surroundings, maintaining a constant temperature throughout the expansion or compression of the gas. However, since the system described is thermally insulated, there is no heat exchange with the surroundings. Therefore, an isothermal process is not applicable.
Adiabatic Process: In an adiabatic process, there is no heat exchange, meaning $ q = 0 $. Since the system is thermally insulated (no heat enters or leaves the system), this is indeed an adiabatic process. The gas will expand freely and rapidly into the empty cylinder $B$.
Isochoric Process: An isochoric process involves a constant volume with no change in volume, often involving heat transfer resulting in changing pressure and temperature. Here, the volume is changing as the gas expands into the evacuated cylinder $B$. Thus, this process is not isochoric.
Isobaric Process: In an isobaric process, the pressure of the system remains constant as volume changes. As the gas expands into the evacuated cylinder $B$, the pressure will decrease in $A$ and increase in $B$, but it will not remain constant. Therefore, this is not an isobaric process.

From the above explanations, the correct option is the adiabatic process, ensuring no heat exchange occurs in this insulated system.

Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stop clock. A contains an ideal gas at standard temperature and pressure. $B$ is completely evacuated. The entire system is thermally insulated. The stop clock is suddenly opened. The process is:

The Correct Option is B

Solution and Explanation

Top Questions on Thermodynamics

Questions Asked in NEET (UG) exam