
Concept explainers
(a)
Interpretation:
The cylinder that best represents the change in the volume of the ideal gas in cylinder A if the pressure is doubled at constant temperature and
Concept introduction:
The
Here,
For two different values of pressure, temperature, volume and number of moles equation (1) can be modified as follows:
Here,
(a)

Answer to Problem 5.142P
Cylinder B correctly represents the change in the volume of the ideal gas.
Explanation of Solution
The temperature and number of moles of gas is fixed and the pressure is doubled.
At constant temperature and number of moles equation (2) can be written as:
Consider the initial pressure be
Rearrange the equation (3) for
Substitute the value
As the pressure is doubled, the volume is decreased to half of the original volume. Therefore cylinder B best represents the change.
As pressure is doubled, the volume is decreased to half of the original volume. The cylinder that indicates the volume half of the volume in cylinder A is cylinder B. Therefore, cylinder B correctly represents the change in the volume of the ideal gas when the pressure of the gas is doubled.
(b)
Interpretation:
The cylinder that best represents the change in the volume of the ideal gas in cylinder A if the temperature is decreased from
Concept introduction:
The ideal
Here,
For two different values of pressure, temperature, volume and number of moles equation (1) can be modified as follows:
Here,
(b)

Answer to Problem 5.142P
Cylinder B correctly represents the change in the volume of the ideal gas.
Explanation of Solution
The pressure and number of moles of gas is fixed and the temperature is halved.
At constant pressure and number of moles equation (2) can be written as:
Rearrange equation (5) for
Substitute the value
As the temperature is decreased by a factor of 2, the volume is decreased to half of the original volume. Therefore cylinder B best represents the change
As the temperature is decreased by a factor of 2, the volume is decreased to half of the original volume. The cylinder that indicates the volume half of the volume in cylinder A is cylinder B. Therefore, cylinder B correctly represents the change in the volume of the ideal gas when the pressure of the gas is doubled.
(c)
Interpretation:
The cylinder that best represents the change in the volume of the ideal gas in cylinder A if the temperature is increased from
Concept introduction:
The ideal gas law equation is as follows:
Here,
For two different values of pressure, temperature, volume and number of moles equation (1) can be modified as follows:
Here,
(c)

Answer to Problem 5.142P
None of the cylinders show volume increases of
Explanation of Solution
Moles and pressure are constant.
The formula to convert
Substitute
Substitute
Substitute the value
As the temperature is increased, the volume is increased by a factor of
As the temperature is increased by a factor of 2, the volume is increased of
(d)
Interpretation:
The cylinder that best represents the change in the volume of the ideal gas in cylinder A if
Concept introduction:
The ideal gas law equation is as follows:
Here,
For two different values of pressure, temperature, volume and number of moles equation (1) can be modified as follows:
Here,
(d)

Answer to Problem 5.142P
Cylinder C correctly represents the change in the volume of the ideal gas.
Explanation of Solution
The temperature and pressure are constant.
Consider the initial moles be
At constant pressure and temperature equation (2) can be written as:
Rearrange equation (8) for
Substitute the value
As moles are increased, the volume is increased by a factor of 2 of the original volume. Therefore cylinder C best represents the change.
As moles are increased, the volume is increased by a factor of 2 of the original volume. The cylinder that indicates the volume double of the volume in cylinder A is cylinder C. Therefore cylinder C best represents the change.
(e)
Interpretation:
The cylinder that best represents the change in the volume of the ideal gas in cylinder A if
Concept introduction:
The ideal gas law equation is as follows:
Here,
For two different values of pressure, temperature, volume and number of moles equation (1) can be modified as follows:
Here,
(e)

Answer to Problem 5.142P
Cylinder D correctly represents the change in the volume of the ideal gas.
Explanation of Solution
Consider the initial moles will be
Consider the initial pressure will be
The temperature is constant.
At constant temperature equation (2) can be written as:
Rearrange equation (10) for
Substitute the value
As moles and pressure are increased, the final volume has the same same as of initial volume. Therefore cylinder D best represents the change.
As moles and pressure are increased, the final volume has the same as of initial volume. The cylinder that indicates the volume same of the volume in cylinder A is cylinder D. Therefore cylinder D best represents the change.
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