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 $b \to c$?


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    $\begingroup$ Hi @samuel. If you found my answer useful, you can check it as the official answer. Otherwise, you can comment and explain why the answer doesn't help you solve the problem (are there additional confusions, etc.). $\endgroup$ – Cicero May 17 '15 at 18:38

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 ($U = nc\Delta T$).


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