Triangular cyclic process I am currently studying for my physics exam and I am trying to wrap my head around cyclic processes.
There is the cyclic process:

We know its an diatomic ideal gas, and the following variables are known for the system.
$$T_a = 200\,\mathrm K,\quad V_a = 1.0\,\mathrm m^3,\quad V_c = 3.0\,\mathrm m^3,\quad P_a = 2.5\,\mathrm{kPa},\quad P_b = 7.5\,\mathrm{kPa}$$
How do I find the growth of internal energy in the process $b \to c$?
 A: The growth of internal energy or change in internal energy can be determined by the following equations

$\Delta U = W + \Delta Q$ or $U = nc\Delta T$, with c being specific heat at constant volume

Now, W is zero since the volume hasn't changed ($W = \int P dV $), so all that is needed is to determine change in heat energy. Heat energy added is equal to $nc\Delta T$ for constant volume, so the first equation reduces to the second equation.
From your information and $PV = nRT$, we can determine the number of moles at point a, and after that the temperature at b, meaning that we can find $n$ and $\Delta T$, leaving us only to find the specific heat at constant volume to find the internal energy. 
Now, the specific heat at constant volume for a diatomic ideal gas can be determined by the following equation

$c = \frac{f}{2} R = 2.5R$, since a diatomic ideal gas has 5 degrees of freedom.

With the specific heat, number of moles and temperate change ($c$, $n$, and $\Delta T$), all that need to be done is to multiply these terms (second equation) to get the growth in internal energy ($U = nc\Delta T$).
