- #1

fluidistic

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## Homework Statement

Two moles of a monoatomic ideal gas expand adiabatically from a temperature [itex]T_i=0°C[/itex] and a pressure of 1 atm until the temperature reaches [itex]T=-50°C[/itex].

1)What are the initial and final volumes and the final pressure of the system?

2)Calculate the work done by the gas. What are the initial and final internal energies of the gas?

## Homework Equations

I)PV=NRT

II)[itex]U=\frac{3RT}{2}[/itex].

III)[itex]PV^{3/2}=constant[/itex]

## The Attempt at a Solution

1)Using I), I get that [itex]P_f V_f=3707.81J[/itex].

Using III), I get that [itex]P_f V_f ^{3/2}=P_i V_i ^{3/2}=45400J[/itex].

Then I isolated [itex]P_f[/itex] from I), plugged into III) and isolated [itex]V_f[/itex] to get [itex]V_f=3.5 m^3[/itex].

This gives me [itex]P_f \approx 1059.61 Pa[/itex] or 0.01 atm. The answer of another student is 0.6 atm. What did I do wrong?!

2)Since the process is adiabatic, there's no heat exchenge of the system with the environment, the change in internal energy is worth the work done on the gas. Using II), I get that the work done by the system is worth 297.9 cal (multiply by 4.186 to get joules). Initial internal energy[itex]=6808.67J[/itex] and final internal energy=[itex]5561.67J[/itex]. Again, the difference is the work done.

Are these numbers correct for part 2)?