An ideal monatomic gas initially has a temperature of 333 K and a pressure of 7.15 atm. It is to expand from volume 581 cm3 to volume 1360 cm3. If the expansion is isothermal, what are (a) the final pressure (in atm) and (b) the work done by the gas? If, instead, the expansion is adiabatic, what are (c) the final pressure (in atm) and (d) the work done by the gas?

In the isothermal case, P*V = constant = P1 V1.

The work done is Integral P dV
= Integral (P1 V1)dV/V
= P1 V1 ln(V2/V1)

In the adiabatic case,
P*V^(5/3) = constant
(for monatomic gases)
The work is once again Integral P dV, but you get a different answer.
Work = [P1*V1^(5/3)]*Integral dV/V^(5/3)

hey drwl thank u so much. but i didn't get right answer for work done. do i hav to convert pressure to pascal for work done? cn u help me?

To solve this problem, we need to apply the ideal gas law equations and the first law of thermodynamics for isothermal and adiabatic processes. Let's go step by step to find the solutions.

(a) Final Pressure in Isothermal Expansion:
For an isothermal process, the temperature remains constant. We can use the equation:

P1 * V1 = P2 * V2

Where P1 and P2 are the initial and final pressures, and V1 and V2 are the initial and final volumes, respectively.

We are given:
Initial temperature (T1) = 333 K
Initial pressure (P1) = 7.15 atm
Initial volume (V1) = 581 cm^3

Final volume (V2) = 1360 cm^3

Substituting the given values into the equation, we get:
7.15 atm * 581 cm^3 = P2 * 1360 cm^3

Solving for P2:
P2 = (7.15 atm * 581 cm^3) / 1360 cm^3
P2 ≈ 3.06 atm

Therefore, the final pressure in the isothermal expansion is approximately 3.06 atm.

(b) Work done by the gas in Isothermal Expansion:
For an isothermal expansion, the work done by the gas can be calculated using the equation:

W = nRT * ln(V2 / V1)

Where W is the work done, n is the number of moles of the gas (which is not provided in the question), R is the gas constant, and V1 and V2 are the initial and final volumes, respectively.

Since the question does not provide the number of moles (n), we cannot calculate the exact value of work done. However, we can calculate the work done per mole of the gas.

Work done per mole = W / n

(c) Final Pressure in Adiabatic Expansion:
For an adiabatic process, there is no heat exchange with the surroundings. Adiabatic expansion can be described by the equation:

P1 * V1^γ = P2 * V2^γ

Where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and γ is the heat capacity ratio, equal to Cp/Cv for a monatomic gas, which is approximately 5/3.

We are given:
Initial pressure (P1) = 7.15 atm
Initial volume (V1) = 581 cm^3
Final volume (V2) = 1360 cm^3
Heat capacity ratio (γ) = 5/3

Substituting the given values into the equation, we get:
7.15 atm * (581 cm^3)^γ = P2 * (1360 cm^3)^γ

Solving for P2:
P2 = (7.15 atm * (581 cm^3)^γ) / (1360 cm^3)^γ
P2 ≈ 3.89 atm

Therefore, the final pressure in the adiabatic expansion is approximately 3.89 atm.

(d) Work done by the gas in Adiabatic Expansion:
For an adiabatic expansion, the work done by the gas can be calculated using the equation:

W = (P2 * V2 - P1 * V1) / (γ - 1)

where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and γ is the heat capacity ratio (5/3 for monatomic gas).

Substituting the given values into the equation, we have:
W = (3.89 atm * 1360 cm^3 - 7.15 atm * 581 cm^3) / (5/3 - 1)

Therefore, use the above equation to calculate the work done by the gas in the adiabatic expansion.