Question

The volume of a gas varies directly with its temperature and inversely with the pressure. If the volume of a certain gas is 15 cubic feet at a temperature of 300 K and a pressure of 40 pounds per square inch, what is the volume of the same gas at 320 K when the pressure is 20 pounds per square inch?

Answer 1

Answer:

Therefore the volume of the gas is 32 cubic feet.

Step-by-step explanation:

Given that,

The volume of a gas varies directly with its temperature and inversely with the pressure.

$V\propto \frac{T}{P}$

V= Volume of the gas at constant mass

T= Temperature at constant mass

P= pressure at constant mass

$\frac{V_1}{V_2}=\frac{\frac{T_1}{T_2}}{\frac{P_1}{P_2}}$

$\therefore \frac{V_1}{V_2}=\frac{T_1P_2}{T_2P_1}$.

Given that,

At constant mass, the volume of a certain gas is 15 cubic feet and a pressure of 40 pound per square inch at a temperature 300 k.

$V_1$=15 cubic feet, $P_1$=40 pound per square inch and $T_1$= 300 K

$V_2=?$, $P_2$=20 pound per square inch and $T_2$= 320k

$\therefore \frac{V_1}{V_2}=\frac{T_1P_2}{T_2P_1}$.

Plugging all values

$\frac{15}{V_2}=\frac{300\times 20}{320\times 40}$

$\Rightarrow V_2=\frac{15\times 320\times 40}{300\times 20}{}$

$\Rightarrow V_2=32$ cubic feet

Therefore the volume of the gas is 32 cubic feet.