Hi Everyone
Does anyone know how I should use this equation to find "W"? the equation is W = mRln(V2 / V1) = (T1 - T3) I originally thought that maybe w equalled mRln(V2 / V1) or (T1 - T3), but they give different awnsers. Can anyone help?

I don't understand where you got that expression from.

I'm a bit rusty with thermo so please bear with me. In fact I plan on spending this summer suping up my thermo skills. The Carnot cyle consists of two types of curves, and adiabat compression/expansion (a proces in which no heat flows) and an isothermal compression/expansion. (process for which the temperature is constant). The total work done in a Carnot cyle equals the area enclosed by the carnot cycle.

The cycle consists of

(1) Isothermal compression from V_a to V_b.
(2) Adiabatic compression from V_b to V_c.
(3) Isothermal expansion from V_c to V_b.
(4) Adiabatic expansion from V_b to V_a.

The work done along an isotherm during an isothermal compression is

W_isotherm = mRln(V_f / V_i)

The work done along an adiabat during compression is

W_adiabat = c_v(T2 - T1)

where c_v is the specific heat of the gas at constant volume (I hope I didn't make any errors in the signs here).

The net work done by a gas during a Carnot cycle is calculated in these notes
http://physics.usask.ca/~plyukhin/ep271/notes/note8.pdf