Question

Consider an ideal gas of 7 moles that is in contact with a thermal reservoir of temperature 475 K. The gas is enclosed in a container that is allowed to expand and contract. If the initial volume of the gas is 0.50 m ³, find the pressure of the gas some time later after the volume has expanded to 1.50 m ³.

Answer 1

Answer:

(a). The initial pressure is $5.5\times10^{4}\ Pa$

(b). The final pressure is $1.8\times10^{4}\ Pa$

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

$P_{i}=\dfrac{nRT_{i}}{V_{i}}$

Put the value into the formula

$P_{i}=\dfrac{7\times8.31\times475}{0.50}$

$P_{i}=55261.5\ Pa$

$P_{i}=5.5\times10^{4}\ Pa$

We need to calculate the final pressure

Using formula of pressure

$P_{f}V_{f}=nRT_{f}$

After expansion,

$\dfrac{P_{f}V_{f}}{P_{i}V_{i}}=\dfrac{nRT_{f}}{nRT_{i}}$

$P_{f}=\dfrac{T_{f}}{T_{i}}\times\dfrac{P_{i}V_{i}}{V_{f}}$

Put the value into the formula

For thermal process,

$T_{i}=T_{f}$

$P_{f}=\dfrac{5.5\times10^{4}\times0.50}{1.50}$

$P_{f}=18333.33\ Pa$

$P_{f}=1.8\times10^{4}\ Pa$

Hence, (a). The initial pressure is $5.5\times10^{4}\ Pa$

(b). The final pressure is $1.8\times10^{4}\ Pa$