Solve the problem. Round to the nearest tenth unless indicated otherwise.
-The volume of a gas varies inversely as the pressure and directly as the temperature (in degrees Kelvin). If a certain gas occupies a volume of $2.3$ liters at a temperature of $320 \mathrm {~K}$ and a pressure of 18 newtons per square centimeter, find the volume when the temperature is $288 \mathrm {~K}$ and the pressure is 9 newtons per square centimeter.
A) $4.1 \mathrm {~L}$
B) $46.0 \mathrm {~L}$
C) $40.9 \mathrm {~L}$
D) $1.3 \mathrm {~L}$

Question

Quizplus · Accepted Answer

The volume of a gas varies inversely with pressure and directly with temperature, which can be represented by the formula $V = k \frac{T}{P}$, where $V$ is volume, $T$ is temperature, $P$ is pressure, and $k$ is a constant. Given $V_1 = 2.3$ L, $T_1 = 320$ K, $P_1 = 18$ N/cm$^2$, and the conditions $T_2 = 288$ K, $P_2 = 9$ N/cm$^2$, we find the new volume $V_2$ by setting up the proportion $\frac{2.3}{V_2} = \frac{320 \times 18}{288 \times 9}$. Solving for $V_2$ gives approximately $4.1$ L.

Solve the Problem 2.32.32.3 Liters at a Temperature Of 320 K320 \mathrm {~K}320 K

Solve the Problem $2.3$ Liters at a Temperature Of $320 \mathrm {~K}$