Chapter 13, Problem 29P

To determine

To calculate: The volume of the ideal gas if the temperature is increases at STP.

Answer to Problem 29P

The volume of the ideal gas if the temperature is increases at STP $1.07{\text{m}}^{\text{3}}$ .

Explanation of Solution

Given:

Initial volume of ideal gas $V_1=3.00{\text{m}}^{\text{3}}$

Initial pressure of ideal gas $P_1=1\text{atm}$

Final pressure of ideal gas $P_2=3.20\text{atm}$

Initial temperature of the ideal gas $T_1=273\text{K}$

Final temperature of the ideal gas $T_2=273\text{K}+38\text{K}=311\text{K}$

Formula used:

According to the Ideal gas equation,

  $R=\frac{PV}{T}$

Considering the above expression for initial and final state.

  $\begin{array}{l}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\\ V_2=V_1\frac{P_1{T}_2}{P_2{T}_1}\end{array}$

Here, $R$ is the universal gas constant,

  $P_1$ is the initial pressure of the ideal gas,

  $V_1$ is the initial volume of ideal gas,

  $P_2$ is the final pressure of ideal gas,

  $T_1$ is the initial temperature of the ideal gas,

  $T_2$ is the final temperature of the ideal gas.

Calculation:

Substitute the values in the given expression.

  $\begin{array}{c}{V}_2=V_1\frac{P_1{T}_2}{P_2{T}_1}\\ =(3.00{\text{m}}^{\text{3}})\left(\frac{1.00\text{atm}}{3.20\text{atm}}\right)\left(\frac{(273+38)\text{K}}{273\text{K}}\right)\\ =1.07{\text{m}}^{\text{3}}\end{array}$

Conclusion:

The volume of the gas at STP is increase by the volume $1.07{\text{m}}^{\text{3}}$ .