Boyle's law: At constant temperature of the gas, the volume of a given mass of a gas is inversely proportional to its pressure.
So, Boyle's law is talking about isothermal condition,right? But, what if temperature is not constant?
My thinking:
Suppose, there is a given gas in a frictionless cylinder fitted with a piston. Its initial temperature is $t_0$ and its pressure is $p_0$ . It is at equilibrium initially and hence the piston will also exert pressure $p_0$ so as to maintain mechanical equilibrium. Now heat is applied to it by a burner. As the gas gains thermal energy, the gas' temperature increases from $t_0$ to $t_k$ . Now as the molecules have more KE, the pressure exerted by the gas on the piston will be more now. And the gas will expand now as a result of which volume increases. But now, the pressure of the gas is low now as the KE is used to displace the piston. And so finally, we can write $$P\propto \frac{1}{v}$$ which is what Boyle's law says but temperature being same.
So, what is the importance of constant temperature?? The gas still follows the law even if temperature is variant. Or am I mistaking anywhere?? Please help. I am confused.
Best Answer
Suppose you compress a piston of gas, while decreasing its temperature drastically. You will find that as $V$ decreases, $P$ decreases as well, so $P$ is no longer proportional to $\frac{1}{V}$ .
Example: Initial state:$V = 1~\text{L}$, $T = 300~\text{K}$, $P = 1~\text{bar}$
Final state: $V = 0.5~\text{L}$, $T = 50~\text{K}$, $P = 0.3~\text{bar}$