How Does a Monatomic Ideal Gas Behave When Heated and Compressed in a Cycle?

[Jeffopolis]

Suppose 1.2 mol of a monatomic ideal gas initially at 11 L and 300 K is heated at constant volume to 590 K, allowed to expand isothermally to its initial pressure, and finally compressed at constant pressure to its original volume, pressure, and temperature. During the cycle, what are (a) the net energy entering the system (the gas) as heat and (b) the net work done by the gas? (c) What is the efficiency of the cycle?

ok so here's what i got, (Ta, Va, refer to point a's temp, volume, etc) did some work and i figured these numbers out

Pa= .40625atm = 41163.28 Pa
Va= .0042 cubic meters
Ta= 21 Kelvin
Pb= 13atm = 1317225 Pa
Vb= .0042 cubic meters
Tb= 666 Kelvin
Pc= .40625 atm = 41163.28 Pa
Vc= .0336 cubic meters
Tc= 166 Kelvin

Now, I am not sure if I am using the right formulas?

DeltaE (internal energy) = (3/2)nRT ?
Q = nC DeltaT ?
W = nC DeltaT ?

I'm not sure if i wrote them wrong in my notes or something, but is this not how you get the heat, work, energy for each transition?

And then, after the full cycle, DeltaE should = 0 correct?Also, i need to get this answered asap as i have a lab writeup due tomorrow... given volume, diameter of a cylinder, initial room pressure, how do you find the pressure of a gas inside said cylinder?

 

[jbsteele]

To find the pressure of a gas inside a cylinder, you need to use the ideal gas law. The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is temperature. You can rearrange this equation to solve for P, giving P = (nRT)/V. So, if you know the volume, number of moles, temperature, and ideal gas constant, you can calculate the pressure of the gas inside the cylinder.