Temperature, Ideal Gases, and Kinetic Theory
- a.) The surface temperature of the sun is about 5750 K. What is this temperature in the Fahrenheit scale?
- (b.) One of the hottest temperatures ever recorded on the surface of Earth was 134oF in Death Valley, CA. What is this temperature in the Celsius scale? What is this temperature in the Kelvin scale?
- (c.) At what temperature do the Fahrenheit and Kelvin scales have the same numerical value?
Hint: Write down one of the two equations for converting from one of these scales to the other and think about how you can make the left hand side of the equation equal to the right hand side. Try out some numerical values and/or use algebraic manipulations.
Problem 2. 7.5 mol of helium are in a 15 L cylinder. The pressure gauge on the cylinder reads 65 psi. Note: Gauge Pressure is defined as absolute pressure minus atmospheric pressure (1 atm). This is because gauge pressure is zero-referenced against ambient air pressure.
(a.) What is the temperature of the gas in oC?
(b.) What is the average kinetic energy of a helium atom?
Problem 3. Total lung capacity of a typical adult is approximately 5.0 L. Approximately 20% of the air is oxygen. At sea level and at an average body temperature of 37 oC, how many moles of oxygen do the lungs contain at the end of an inhalation?
Problem 4. The gauge pressure in your car tires is 2.50 × 105 N/m2 at a temperature of 35.0 oC when you drive onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to −40.0 oC? Recall: Gauge Pressure is defined as absolute pressure minus atmospheric pressure (1 atm).
Problem 5. Much of the gas near the Sun is atomic hydrogen. (Note that the atomic mass of hydrogen is m(1H)=1u=1.66×10−27 kg)
(a.) What is the average kinetic energy (in Joules) of hydrogen atoms on the 5500oC surface of the Sun? (b.) What is the average velocity vrms of the hydrogen atoms?
Problem 6. An ideal gas is at 20 oC.
If we double the average kinetic energy of the ga