Chapter 5, Problem 5.29QP

(a)

Interpretation Introduction

Interpretation:

Automobile tires are flatter on cold days has to be explained

Concept Introduction:

Ideal gas equation:

At a constant temperature (K) and pressure (P), the volume (v) occupied by the no of moles of any gas is known as ideal gas equation.

Ideal gas equation:

$\text{PV}\text{=}\text{nRT}$

And the SI units are

$\begin{array}{l}\text{T= Temperature }\left({\text{273}}^{\text{0}}\text{K}\right)\text{ = Kelvin}\\ \text{n = no of moles}\left(\text{1}\text{mole =}\text{6}{\text{.023×10}}^{\text{23}}\text{atoms}\right)\text{ = mole}\\ \text{V= Volume }\left(\text{22}\text{.4 L}\right)\text{ = cubic}\text{meter}\left({\text{m}}^{\text{3}}\right)\\ \text{P = Pressure }\left(\text{1}\text{atm}\right)\text{ = pascal(Pa)}\\ \text{R= universal gas constant }\left(\text{8}\text{.314 }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\right)\text{ = }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\end{array}$

Answer to Problem 5.29QP

The amount of air and volume of the tire in the tire remains unchanged.

Explanation of Solution

From Ideal gas equation, $\text{PV}\text{=}\text{nRT}$ we can observe that pressure is directly proportional to temperature, so on a cold day i.e., when temperature decreases the pressure in the tire flatter that means pressure decreases.

Conclusion

Automobile tires are flatter on cold days was explained.

(b)

Interpretation Introduction

Interpretation:

Why Aerosol cans are not supposed to dispose in fire has to be explained.

Concept Introduction:

Ideal gas equation:

At a constant temperature (K) and pressure (P), the volume (v) occupied by the no of moles of any gas is known as ideal gas equation.

Ideal gas equation:

$\text{PV}\text{=}\text{nRT}$

And the SI units are

$\begin{array}{l}\text{T= Temperature }\left({\text{273}}^{\text{0}}\text{K}\right)\text{ = Kelvin}\\ \text{n = no of moles}\left(\text{1}\text{mole =}\text{6}{\text{.023×10}}^{\text{23}}\text{atoms}\right)\text{ = mole}\\ \text{V= Volume }\left(\text{22}\text{.4 L}\right)\text{ = cubic}\text{meter}\left({\text{m}}^{\text{3}}\right)\\ \text{P = Pressure }\left(\text{1}\text{atm}\right)\text{ = pascal(Pa)}\\ \text{R= universal gas constant }\left(\text{8}\text{.314 }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\right)\text{ = }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\end{array}$

Explanation of Solution

From Ideal gas equation, $\text{PV}\text{=}\text{nRT}$ we can observe that pressure is directly proportional to temperature, Aerosol cans having fixed volume and fixed amount of gas filled at constant temperature in it. When temperature increases the pressure in the can increases and can gets exploded.

Conclusion

Aerosol cans are not supposed to dispose in fire was explained.

(c)

Interpretation Introduction

Interpretation:

The lid of a water bottle pops off when the bottle sits in the sun has to be explained.

Concept Introduction:

Ideal gas equation:

At a constant temperature (K) and pressure (P), the volume (v) occupied by the no of moles of any gas is known as ideal gas equation.

Ideal gas equation:

$\text{PV}\text{=}\text{nRT}$

And the SI units are

$\begin{array}{l}\text{T= Temperature }\left({\text{273}}^{\text{0}}\text{K}\right)\text{ = Kelvin}\\ \text{n = no of moles}\left(\text{1}\text{mole =}\text{6}{\text{.023×10}}^{\text{23}}\text{atoms}\right)\text{ = mole}\\ \text{V= Volume }\left(\text{22}\text{.4 L}\right)\text{ = cubic}\text{meter}\left({\text{m}}^{\text{3}}\right)\\ \text{P = Pressure }\left(\text{1}\text{atm}\right)\text{ = pascal(Pa)}\\ \text{R= universal gas constant }\left(\text{8}\text{.314 }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\right)\text{ = }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\end{array}$

Explanation of Solution

When water bottle sits in the sun, the liquid water gains temperature, as the temperature of water increases the vapor pressure also increases. If the pressure increases it will topple the lid of the bottle.

Conclusion

The lid of a water bottle pops off when the bottle sits in the sun was explained.

(d)

Interpretation Introduction

Interpretation:

Balloon pops up when we squeezes it has to be explained.

Concept Introduction:

Ideal gas equation:

At a constant temperature (K) and pressure (P), the volume (v) occupied by the no of moles of any gas is known as ideal gas equation.

Ideal gas equation:

$\text{PV}\text{=}\text{nRT}$

And the SI units are

$\begin{array}{l}\text{T= Temperature }\left({\text{273}}^{\text{0}}\text{K}\right)\text{ = Kelvin}\\ \text{n = no of moles}\left(\text{1}\text{mole =}\text{6}{\text{.023×10}}^{\text{23}}\text{atoms}\right)\text{ = mole}\\ \text{V= Volume }\left(\text{22}\text{.4 L}\right)\text{ = cubic}\text{meter}\left({\text{m}}^{\text{3}}\right)\\ \text{P = Pressure }\left(\text{1}\text{atm}\right)\text{ = pascal(Pa)}\\ \text{R= universal gas constant }\left(\text{8}\text{.314 }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\right)\text{ = }\frac{\text{joule}}{\text{mole}\text{.kelvin}}\end{array}$

Explanation of Solution

From the ideal gas equation, $\text{PV}\text{=}\text{nRT}$ we know that pressure and volume are inversely proportional to each other, when we squeeze the balloon the volume will decrease and pressure will increases, when balloon exerts at most pressure the balloon pop out.

Conclusion

Balloon pops up when we squeezes it was explained.