- #1

LightofAether

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*real*thermodynamics class, so I'm not entirely sure what I'm doing. Any help is greatly appreciated!

## Homework Statement

A rigid horizontal cylinder contains a freely moving piston. Initially, it divides the cylinder into equal volumes, and each side of the piston contains 1 mole of an ideal gas at 5°C and 1 bar. An electrical resistance heater is installed on side A (left side) of the piston, and is energized to slowly heat the gas on side A to 170°C. If the tank and the piston are perfect insulators, calculate the heat added to the system by the resistance heater. The molar heat capacities of the gas are: C

_{v}= (3/2) R and C

_{p}= (5/2)R. (Hint: choose your system wisely.)

## Homework Equations

[tex]PV=nRT[/tex] [tex]\Delta U = W + Q[/tex] [tex]\Delta U = nC_v\Delta T[/tex] [tex]P = P_i (v_i/v_f)^\lambda[/tex]

## The Attempt at a Solution

First I started off by converting the known data into the proper units and calculated the initial volume of each side using the ideal gas law.

[tex]T_Ai = T_Bi = 278 K[/tex] [tex]P_Ai = P_Bi = 1*10^5 N/m^2[/tex] [tex]n_Ai = n_Bi = 1 mol[/tex] [tex]T_Af = 443K[/tex] [tex]V_Ai = V_Bi = 0.023 m^3[/tex]

Now onto choosing a system. I'm torn on whether to choose A or B. Side B is adiabatic so I could use this equation [tex]P = P_i (v_i/v_f)^\lambda[/tex], but I don't know have a way to find the final volume of B. Side A is not adiabatic so I'm left with [tex]\Delta U = W + Q[/tex] and [tex]\Delta U = nC_v\Delta T[/tex], but like side B I don't have a way to find the final volume to calculate the work being done.

A push in the right direction would be awesome. The assigned textbook for this class has proven to be very unhelpful.