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

32

Explanation:

Answer 2

Therefore the volume of the gas is 32 cubic feet.

Explanation:

Given that,

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

`V\propto (T)/(P)`

V= Volume of the gas at constant mass

T= Temperature at constant mass

P= pressure at constant mass

`(V_1)/(V_2)=((T_1)/(T_2))/((P_1)/(P_2))`

`\therefore (V_1)/(V_2)=(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 (V_1)/(V_2)=(T_1P_2)/(T_2P_1)`.

Plugging all values

`(15)/(V_2)=(300* 20)/(320* 40)`

`\Rightarrow V_2=(15* 320* 40)/(300* 20){}`

`\Rightarrow V_2=32` cubic feet

Therefore the volume of the gas is 32 cubic feet.