Please show work for everything either below or to the right of the problem. A glass cylinder filled with \( n = 0.91 \) mol of air is capped with a moveable piston that can slide frictionlessly inside the cylinder. The gas is adiabatically compressed by rapidly slamming the piston down into the cylinder with a constant force \( F = 190 \, \text{N} \) over a distance of \( d = 14 \, \text{cm} \). What is the change in temperature \( \Delta T \) of the gas? Draw a PV diagram of this process as part of your representation; make sure it includes the adiabatic process, isothermal lines corresponding to the initial and final temperatures, and shading that corresponds to the work done on/by the gas. For the limit check, investigate what happens to \( \Delta T \) if the piston is pushed only a very short distance into the cylinder \( (d \rightarrow 0) \).

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A glass cylinder filled with n = 0.91 mol of air is capped with a moveable piston that can slide frictionlessly inside the cylinder. The gas is adiabatically compressed by rapidly slamming the piston down into the cylinder with a constant force F = 190 N over a distance of d = 14 cm. What is the change in temper- ature AT of the gas? Draw a PV diagram of this process as part of your representation; make sure it includes the adiabatic process, isothermal lines corresponding to the initial and final temperatures, and shading that corresponds to the work done on/by the gas. For the limit check, investigate what happens to AT if the piston is pushed only a very short distance into the cylinder (d→ 0).

A glass cylinder filled with n = 0.91 mol of air is capped with a moveable piston that can slide frictionlessly inside the cylinder. The gas is adiabatically compressed by rapidly slamming the piston down into the cylinder with a constant force F = 190 N over a distance of d = 14 cm. What is the change in temper- ature AT of the gas? Draw a PV diagram of this process as part of your representation; make sure it includes the adiabatic process, isothermal lines corresponding to the initial and final temperatures, and shading that corresponds to the work done on/by the gas. For the limit check, investigate what happens to AT if the piston is pushed only a very short distance into the cylinder (d→ 0).