Question

the pressure of a fixed mass of gas is 2.0×10^5 n per m^2 at a known temperature. assuming that the temperature remains constant, what will be the pressure of the gas if its volume is halved? 3.0×10^5 n per m^2 1.0×10^5 n per m^2 2.0×10^5 n per m^2 4.0×10^5 n per m^2

Explanation:

Step1: Recall Boyle's law

For a fixed - mass of gas at constant temperature, $P_1V_1 = P_2V_2$.

Step2: Let initial pressure $P_1$ and volume $V_1$

Given $P_1=2.0\times 10^{5}\ N/m^{2}$, and $V_2=\frac{1}{2}V_1$.

Step3: Substitute into Boyle's law

$P_1V_1 = P_2\times\frac{1}{2}V_1$.

Step4: Solve for $P_2$

Cancel out $V_1$ on both sides, we get $P_2 = 2P_1$.
$P_2=2\times(2.0\times 10^{5}\ N/m^{2})=4.0\times 10^{5}\ N/m^{2}$.

Answer:

$4.0\times 10^{5}\ N/m^{2}$