Question

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

Answer 1

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

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

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:

`\begin{gathered} (P_1V_1)/(T)=(P_2\cdot4V_1)/(T)\\ \\ P_1=4P_2\\ \\ P_2=(P_1)/(4) \end{gathered}`

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

Therefore the correct option is 1).