Pressure vs Vlume graph questions

[joemama69]

Homework Statement

0.20 moles of a monatomic ideal gas is initially at a temperature of –23 0C.
Call this state “A.” The gas is now compressed slowly and adiabatically to
state “B” in which it has one third of its initial volume. Next it is isothermally
expanded back to its initial volume in state “C.” Finally it undergoes a
constant volume process that returns it to its initial state.

a) Sketch this cyclic process with reasonable care on a PV diagram and
label the three states—A, B, and C.

b) Show that the temperature of state B is 247 0C.

c) Find the heat input to the gas along each leg of the cycle—QAB, QBC,
and QCA. [Note: Use the result of part b whether or not you got it!]

d) Use the results of part c) and the first law of thermodynamics to find the
net work done by the gas around the entire cycle.

Homework Equations

The Attempt at a Solution

Part A) Note the attachment. Its a little crude but the two lines (ab) & (bc) are suppose to nice curves

Part B) I'm not really sure what formula to use here. Because the temp changes I know i can't use and of the PV formulas. Heres what I know...

T_o = 250 Kelvin, T = 520 Kelvin, V = 1/3 V_o, Q = 0

 

[joemama69]

oops forgot the attachment.

Should i be using

PV - P_oV_o = Nk(T - T_o) and solve for T

first i need to find P

PV = P_oV_o ...P(1/3 V_o) = P_o V_o... P = 3P_o

3P(1/3V) - PV = Nk(T - 250) where N = .2*6.02E^23 & k = 1.38E^-23

0 = NkT - NK250 this is not right what ami doing wrong