A cylinder filled with n $=1\mathrm{.}5$ mol of air is capped with a move$-$

able piston, which can slide frictionlessly inside the cylinder.

The air, which you can model as an ideal diatomic gas, is ini$-$

tially at room temperature $($Ti $=295$ K$).$ The piston is given a

brief, downward whack with a hammer, causing the air inside

the cylinder to compress adiabatically. The person swinging

the hammer does W $=550$ J of work on the gas in getting

it to its final state of maximum compression. What is the

final temperature Tf of the gas? For the limit check, inves$-$

tigate what happens to Tf if the whack from the hammer is

extremely weak, meaning that the person swinging it does very

little work on the gas $($W $0).$ For your representation, draw

this process on the P V plane. Make sure to include isother$-$

mal curves representing the initial$/$final temperatures, as well

as an adiabatic curve representing the process that occurred.

Representation: $012$

Physics Concept$($s$)$: $012$

Initial Equation$($s$)$: $00\mathrm{.}51$

Symbolic Answer: $01$

Units Check: $00\mathrm{.}51$

Limits Check: $00\mathrm{.}51$

Neatness: $-2-10$

Total:

Correct Answer: Y N

Representation

Physics Concept$($s$)($Refer to the list posted on Carmen$)$ Initial Equations

$(1)$

$(2)$

$$ Show Your Equation Work On Next Page $$

Algebra Work $($Symbols only. Don$$t plug in any numbers yet.$)$

Symbolic Answer:

Unit Check Limit Check

a$)$ As W $0,$ what limit does Tf approach?

b$)$ Why does the result make physical sense?

Numerical Answer: $($Obtain this by plugging numbers into your symbolic answer.