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.
[tex]V\propto \frac{T}{P}[/tex]
V= Volume of the gas at constant mass
T= Temperature at constant mass
P= pressure at constant mass
[tex]\frac{V_1}{V_2}=\frac{\frac{T_1}{T_2}}{\frac{P_1}{P_2}}[/tex]
[tex]\therefore \frac{V_1}{V_2}=\frac{T_1P_2}{T_2P_1}[/tex].
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.
[tex]V_1[/tex]=15 cubic feet, [tex]P_1[/tex]=40 pound per square inch and [tex]T_1[/tex]= 300 K
[tex]V_2=?[/tex], [tex]P_2[/tex]=20 pound per square inch and [tex]T_2[/tex]= 320k
[tex]\therefore \frac{V_1}{V_2}=\frac{T_1P_2}{T_2P_1}[/tex].
Plugging all values
[tex]\frac{15}{V_2}=\frac{300\times 20}{320\times 40}[/tex]
[tex]\Rightarrow V_2=\frac{15\times 320\times 40}{300\times 20}{}[/tex]
[tex]\Rightarrow V_2=32[/tex] cubic feet
Therefore the volume of the gas is 32 cubic feet.
