Question

Six thermodynamic states of the same monatomic ideal gas sample are represented in the figure. Rank...

Six thermodynamic states of the same monatomic ide

Six thermodynamic states of the same monatomic ideal gas sample are represented in the figure.

Rank these states on the basis of the temperature of the gas sample in each state.

Rank from largest to smallest. To rank items as equivalent, overlap them.

E> F> D> C> B> A IS NOT THE ANSWER


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Answer #1
Concepts and reason

The concept used to solve this problem is the ideal gas equation.

Use the concept of ideal gas to find the temperature of each thermodynamic state.

Use the temperature of each thermodynamic state to rank them from largest to smallest.

Fundamentals

The ideal gas equation or the equation of state is defined as the volume occupied by n number of moles at pressure and temperatureT(Kelvins)
.

PV = nRT

Here, is the pressure of the gas, is the volume of the gas, is the number of moles or the amount of substance, is known as universal gas constant which is the product of Boltzmann constant and Avogadro’s number, and is the absolute temperature of the gas.

Expression for the ideal gas is as follows,

PV = nRT

Rearrange the above expression for .

PV = nRT
nr

Expression for the temperature of the ideal gas is as follows,

T=PV/NR
…… (1)

For state A,

Substitute 2 units
for and 3 units
for .

PV = nRT
(2P)(3V)=nRT,
1=(6)PV/NR

For state B,

Substitute 2 units
for and 6 units
for in equation (1).

PV = nRT,
(2P)(6V)=nRT,
To =(12) PVNR

For state C,

Substitute 4 units
for and 3 units
for in equation (1).

PV = nRT
(4P)(3V)=nRT
Te =(12) PV /nR

For state D,

Substitute 4 units
for and 6 units
for in equation (1).

PV = nRT,
(4P)(6V)=nRT,
To = (24)PV/NR

For state E,

Substitute 4 units
for and 9 units
for in equation (1).

PV = nRT,
(4P)(9V)=nRT,
Ty = (36) PV /nR

For state F,

Substitute 6 units
for and 6 units
for in equation (1).

PV = nRT,
(6P)(6V)=nRT,
To = (36) PV /nR

Compare the temperature of each state and arrange them from largest to smallest.

The order of the temperature of the gas at each state is as follows,

T; ET, >T, >Te =T>T,

Ans:

The descending order of temperature for different states isT, ET, >T, >T. =T>T.
.

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