An ideal, monatomic gas is allowed to expand quasi-statically and adiabatically

Question

An ideal, monatomic gas is allowed to expand quasi-statically and adiabatically from an initial volume Vi = 2.2 liters and initial temperature Ti = 400 K to a final volume of Vf = 5.8 liters. If there are n = 0.5 mol of gas,

find the final temperature Tf.

210. K

What is the final pressure Pf?

1.50×105 Pa

What is the work done by the gas?

1190 J

What is the change in the internal energy of the gas?

-1190 J

Now, suppose that the gas expands quasi-statically and isothermally. Using the same values for Vi, Vf, Ti, and n, calculate the final pressure.

Calculate the heat added to the system in this isothermal expansion.

i need help for the last 2 questions i added the correct answers to the previous questions

Explanation / Answer

the process is isothermal.

so, Tf = Ti = 400 K

Vf = 5.8 L = 5.8*10^-3 m^3

n of moles, n = 0.5

Apply, Pf*Vf = n*R*Tf

==> Pf = n*R*Tf/Vf

= 0.5*8.314*400/(5.8*10^-3)

= 2.87*10^5 pa <<<<<<----------------Answer

workdone by the gas, W = n*R*T*ln(Vf/Vi)

= 0.5*8.314*400*ln(5.8/2.2)

= 1612 J

now use first law of thermodymnamics

dQ = dU + dW

dQ = dW (In isothermal process dU = 0)

= 1612 J <<<<<<----------------Answer

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