diff --git a/Myśli nieuczesane.md b/Myśli nieuczesane.md
index 5e87262..f4196f0 100644
--- a/Myśli nieuczesane.md	
+++ b/Myśli nieuczesane.md	
@@ -6,4 +6,14 @@ For the given sequence $a_n=n^{2}-8n+15$, the first derivative is $a'_n=2n-8$. T
 
 Therefore, the sequence is not monotonic because it is both increasing and decreasing. We can express this in LaTeX as follows:
 
-$a_n=n^{2}-8n+15$ is not monotonic because its first derivative, $a'_n=2n-8$, has both positive and negative values.
\ No newline at end of file
+$a_n=n^{2}-8n+15$ is not monotonic because its first derivative, $a'_n=2n-8$, has both positive and negative values.
+
+
+
+The equation for adiabatic gas expansion is:
+
+$$\frac{dU}{dt} = \frac{PdV}{dt}$$
+
+where $U$ is the internal energy of the gas, $P$ is the pressure of the gas, and $V$ is the volume of the gas. This equation describes the change in the internal energy of the gas as it expands adiabatically, which means that there is no heat transfer between the gas and its surroundings.
+
+$\mathbb{R}$