# Groupwork 5 Adiabatic Cooling

- Page ID
- 63421

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

*Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.*

The figure below from your text, shows several different paths that could be taken as thermodynamic variables, *P*, *T*, and *V*, change.

Path A represents a reversible isothermal expansion/compression.

Path B represents a reversible adiabatic expansion/compression.

Path C completes the cycle.

Consider this diagram for an ideal gas following \(PV=nRT\). Rank the pressure values for \(P_1,P_2,P_3\) from largest to smallest. What is larger, \(V_1\) or \(V_2\)?

What is larger, \(T_1\) or \(T_2\)? Justify your answer.

For Path A, write down an expression describing *dU*_{A}.

For Path B, write down an expression describing *dU*_{B}.

For Path C, write down an expression describing *dU*_{C}.

What is *dU* for the whole cycle, that is Path A to Path B to Path C?

What does this tell you about *dU*_{B} and *dU*_{C}?

Write down mathematical expressions for *dq*_{C} and *dw*_{B}. How are these two expressions related? If you want to integrate *dq*_{C} and *dw*_{B}, how can you simplify the expression so that you have only one variable on each side of the equation?

How are the change in volume and change in temperature related to each other?