Chapter 5, Problem 45Q

To determine

To rank the pressure of each container.

Answer to Problem 45Q

The pressure of the containers is ranked from largest to smallest pressure as,

$P_1>P_3>P_5=P_6>P_4>P_2$.

Explanation of Solution

Container A:

Given info:

The temperature of the container is $200K$.

The volume of the container A is $2000c{m}^3$.

The value of universal gas constant $R$ is $8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}$.

Formula used:

Formula to find the pressure of the container.

Using ideal gas equation,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume of the gas, $n$ number of moles, $R$ universal gas constant and $T$ is the temperature the copper container.

Calculation:

Substitute the given values to find the final equilibrium temperature,

Let container contains one mole of helium gas the pressure is,

$\begin{array}{c}{P}_1=\frac{8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}\times 200K}{2000{\text{cm}}^{\text{3}}}\\ =1.247\text{atm}\end{array}$

Container B:

Given info:

The temperature of the container is $300K$.

The volume of the container B is $15000c{m}^3$.

The value of universal gas constant $R$ is $8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}$.

Formula used:

Formula to find the pressure of the container.

Using ideal gas equation,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume of the gas, $n$ number of moles, $R$ universal gas constant and $T$ is the temperature the copper container.

Calculation:

Substitute the given values to find the final equilibrium temperature,

Let container contains one mole of helium gas the pressure is,

$\begin{array}{c}{P}_2=\frac{8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}\times 300K}{15,000{\text{cm}}^{\text{3}}}\\ =0.1663\text{atm}\end{array}$

Container C:

Given info:

The temperature of the container is $400K$.

The volume of the container C is $5000c{m}^3$.

The value of universal gas constant $R$ is $8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}$.

Formula used:

Formula to find the pressure of the container.

Using ideal gas equation,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume of the gas, $n$ number of moles, $R$ universal gas constant and $T$ is the temperature the copper container.

Calculation:

Substitute the given values to find the final equilibrium temperature,

Let container contains one mole of helium gas the pressure is,

$\begin{array}{c}{P}_3=\frac{8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}\times 300K}{5,000{\text{cm}}^{\text{3}}}\\ =0.499\text{atm}\end{array}$

Container D:

Given info:

The temperature of the container is $300K$.

The volume of the container D is $10,000c{m}^3$.

The value of universal gas constant $R$ is $8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}$.

Formula used:

Formula to find the pressure of the container.

Using ideal gas equation,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume of the gas, $n$ number of moles, $R$ universal gas constant and $T$ is the temperature the copper container.

Calculation:

Substitute the given values to find the final equilibrium temperature,

Let container contains one mole of helium gas the pressure is,

$\begin{array}{c}{P}_4=\frac{8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}\times 300K}{10,000{\text{cm}}^{\text{3}}}\\ =0.249\text{atm}\end{array}$

Container E:

Given info:

The temperature of the container is $200K$.

The volume of the container E is $4000c{m}^3$.

The value of universal gas constant $R$ is $8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}$.

Formula used:

Formula to find the pressure of the container.

Using ideal gas equation,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume of the gas, $n$ number of moles, $R$ universal gas constant and $T$ is the temperature the copper container.

Calculation:

Substitute the given values to find the final equilibrium temperature,

Let container contains one mole of helium gas the pressure is,

$\begin{array}{c}{P}_5=\frac{8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}\times 200K}{4,000{\text{cm}}^{\text{3}}}\\ =0.416\text{atm}\end{array}$

Container F:

Given info:

The temperature of the container is $500K$.

The volume of the container F is $10,000c{m}^3$.

The value of universal gas constant $R$ is $8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}$.

Formula used:

Formula to find the pressure of the container.

Using ideal gas equation,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume of the gas, $n$ number of moles, $R$ universal gas constant and $T$ is the temperature the copper container.

Calculation:

Substitute the given values to find the final equilibrium temperature,

Let container contains one mole of helium gas the pressure is,

$\begin{array}{c}{P}_6=\frac{8.314{\text{ Jmol}}^{\text{-}}{}^{\text{1}}{\text{K}}^{\text{-}}{}^{\text{1}}\times 500K}{10,000{\text{cm}}^{\text{3}}}\\ =0.416\text{atm}\end{array}$

After calculation the pressure of containers is ranked from largest to smallest pressure as,

$P_1>P_3>P_5=P_6>P_4>P_2$.

Conclusion:

Thus, the pressure of the containers is ranked from largest to smallest pressure as,

$P_1>P_3>P_5=P_6>P_4>P_2$.