Respuesta :
Answer :
(a). The final temperature of the gas in the cylinder A is 320 K.
(b). The final temperature of the gas in the cylinder B is 233.7 K.
(c). The final volume of the gas in the cylinder A is [tex]7.86\times10^{-3}\ m^3[/tex]
(d). The final volume of the gas in the cylinder B is [tex]5.7\times10^{-3}\ m^3[/tex]
Explanation :
Given that,
Number of mole n = 0.30 mol
Initial temperature = 320 K
Pressure = 3.0 atm
Final pressure = 1.0 atm
We need to calculate the initial volume
Using formula of ideal gas
[tex]P_{1}V_{1}=nRT[/tex]
[tex]V_{1}=\dfrac{nRT}{P_{1}}[/tex]
Put the value into the formula
[tex]V_{1}=\dfrac{0.30\times8.314\times320}{3.039\times10^{5}}[/tex]
[tex]V_{1}=2.62\times10^{-3}\ m^3[/tex]
(a). We need to calculate the final temperature of the gas in the cylinder A
Using formula of ideal gas
In isothermally, the temperature is not change.
So, the final temperature of the gas in the cylinder A is 320 K.
(b). We need to calculate the final temperature of the gas in the cylinder B
Using formula of ideal gas
[tex]T_{2}=T_{1}\times(\dfrac{P_{1}}{P_{2}})^{\frac{1}{\gamma}-1}[/tex]
Put the value into the formula
[tex]T_{2}=320\times(\dfrac{3}{1})^{\frac{1}{1.4}-1}[/tex]
[tex]T_{2}=233.7\ K[/tex]
(c). We need to calculate the final volume of the gas in the cylinder A
Using formula of volume of the gas
[tex]P_{1}V_{1}=P_{2}V_{2}[/tex]
[tex]V_{2}=\dfrac{P_{1}V_{1}}{P_{2}}[/tex]
Put the value into the formula
[tex]V_{2}=\dfrac{3\times2.62\times10^{-3}}{1}[/tex]
[tex]V_{2}=0.00786\ m^3[/tex]
[tex]V_{2}=7.86\times10^{-3}\ m^3[/tex]
(d). We need to calculate the final volume of the gas in the cylinder B
Using formula of volume of the gas
[tex]V_{2}=V_{1}(\dfrac{P_{1}}{P_{2}})^{\frac{1}{\gamma}}[/tex]
[tex]V_{2}=2.62\times10^{-3}\times(\dfrac{3}{1})^{\frac{1}{1.4}}[/tex]
[tex]V_{2}=0.0057\ m^3[/tex]
[tex]V_{2}=5.7\times10^{-3}\ m^3[/tex]
Hence, (a). The final temperature of the gas in the cylinder A is 320 K.
(b). The final temperature of the gas in the cylinder B is 233.7 K.
(c). The final volume of the gas in the cylinder A is [tex]7.86\times10^{-3}\ m^3[/tex]
(d). The final volume of the gas in the cylinder B is [tex]5.7\times10^{-3}\ m^3[/tex]
