Respuesta :
Answer:
(a). The initial pressure is [tex]5.5\times10^{4}\ Pa[/tex]
(b). The final pressure is [tex]1.8\times10^{4}\ Pa[/tex]
Explanation:
Given that,
Number of moles = 7
Temperature = 475 K
Initial volume = 0.50 m³
Expanded volume = 1.50 m³
We need to calculate the initial pressure
Using formula of pressure
[tex]P_{i}=\dfrac{nRT_{i}}{V_{i}}[/tex]
Put the value into the formula
[tex]P_{i}=\dfrac{7\times8.31\times475}{0.50}[/tex]
[tex]P_{i}=55261.5\ Pa[/tex]
[tex]P_{i}=5.5\times10^{4}\ Pa[/tex]
We need to calculate the final pressure
Using formula of pressure
[tex]P_{f}V_{f}=nRT_{f}[/tex]
After expansion,
[tex]\dfrac{P_{f}V_{f}}{P_{i}V_{i}}=\dfrac{nRT_{f}}{nRT_{i}}[/tex]
[tex]P_{f}=\dfrac{T_{f}}{T_{i}}\times\dfrac{P_{i}V_{i}}{V_{f}}[/tex]
Put the value into the formula
For thermal process,
[tex]T_{i}=T_{f}[/tex]
[tex]P_{f}=\dfrac{5.5\times10^{4}\times0.50}{1.50}[/tex]
[tex]P_{f}=18333.33\ Pa[/tex]
[tex]P_{f}=1.8\times10^{4}\ Pa[/tex]
Hence, (a). The initial pressure is [tex]5.5\times10^{4}\ Pa[/tex]
(b). The final pressure is [tex]1.8\times10^{4}\ Pa[/tex]
