Find the pressure, compared to the original pressure P, if the volume of a given mass of a gas at constant temperature becomes four times larger. Answer choices 1.) P/42.) 4P3.) 8P4.) T/4P

Respuesta :

In order to find the new pressure, we can use the relation below:

[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]

Where P is the pressure, V is the volume and T is the temperature.

If the temperature remains the same and the volume increases four times, we have T1 = T2 = T and V2 = 4V1:

[tex]\begin{gathered} \frac{P_1V_1}{T}=\frac{P_2\cdot4V_1}{T}\\ \\ P_1=4P_2\\ \\ P_2=\frac{P_1}{4} \end{gathered}[/tex]

We can see that the new pressure is 4 times lower than the initial pressure.

Therefore the correct option is 1).