7.9 The ideal gas law  (Page 6/11)

Find out the human population of Earth. Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth?

Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

The gauge pressure in your car tires is $2\text{.}\text{50}\times {\text{10}}^5{\text{N/m}}^2$ at a temperature of $\text{35}\text{.}0\text{º}\text{C}$ when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to $–\text{40}\text{.}0\text{º}\text{C}$ ?

Convert an absolute pressure of $7\text{.}\text{00}\times {\text{10}}^5{\text{N/m}}^2$ to gauge pressure in ${\text{lb/in}}^2\text{.}$ (This value was stated to be just less than $\text{90}\text{.}{\text{0 lb/in}}^2$ in [link] . Is it?)

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of $\text{20}\text{.}0\text{º}\text{C}$ . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is $\text{60}\text{.}0\text{º}\text{C}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?

Large helium-filled balloons are used to lift scientific equipment to high altitudes. (a) What is the pressure inside such a balloon if it starts out at sea level with a temperature of $\text{10}\text{.}0\text{º}\text{C}$ and rises to an altitude where its volume is twenty times the original volume and its temperature is $–\text{50}\text{.}0\text{º}\text{C}$ ? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)

Confirm that the units of $\text{nRT}$ are those of energy for each value of $R$ : (a) $8\text{.}\text{31}\text{J/mol}\cdot \text{K}$ , (b) $1\text{.}\text{99 cal/mol}\cdot \text{K}$ , and (c) $0\text{.}\text{0821 L}\cdot \text{atm/mol}\cdot \text{K}$ .