Kinetic Theory and Thermodynamics Practice

Transcription

1 Kinetic Theory and Thermodynamics Practice 1) State four assumptions needed to explain the relationship between the kinetic energy of the particles that make up an ideal gas and the pressure the ideal gas exerts on the walls of its container. 2) A steam engineʼs boiler can heat water vapour to a temperature of 650 K. Calculate the average kinetic energy of the water molecules at this temperature. 3) Calculate the root-mean-square velocity of the water molecules in the boiler mentioned in Question 2. The mass of a water molecule is 2.99 x g 4) Calculate the temperature required to cause the atoms that make up mercury vapour to achieve a room-mean-square velocity of 98.0 m/s. The molar mass of mercury is 201 g/mol.

2 Use the following information to answer the next four questions. Little Timmyʼs inflated toy T-Rex has been inflated beyond the recommended pressure and the cheap plastic material is starting to slowly stretch. Timmy decides to plot a pressure-volume graph to explain to his sister that work is done by the gas. 5) What does the area under Timmyʼs P-V graph represent? 6) Show using unit analysis that change in pressure multiplied by change in volume is equivalent to work. 7) Timmy is able to measure the following values: " Pi = 10 N/m 2 " Pf = 5.0 N/m 2 " Vi = 1000 L " Vf = 1200 L " Estimate the work done by the gas during the dinosaurʼs expansion. 8) Is the dinosaurʼs expansion isothermal or adiabatic?

3 Use the following information to answer the next question. In a refrigerator, fluid picks heat up from the air in the food storage compartment. The fluid is then rapidly compressed in the The heat pump in a refrigerator rapidly compressed, which causes it to heat up to greater than room temperature. This hotter fluid looses heat as it passes through pipes in the radiator grid on the rear of the of pipes on the rear of the fridge called the radiator. 9) Is this type of compression adiabatic or isothermal?

4 Use the following additional information to answer the next question 10) Below is a graph showing adiabatic expansion. Sketch a similar graph showing adiabatic compression. For both graphs identify whether gasʼs temperature increases or decreases. 11) A cyclist exerts a constant pressure of 50 N/m 2 on the air cylinder in a bicycle pump causing the volume to decrease from 1.0 L to 0.25 L. Calculate the work done by the cyclist on the gas in the cylinder. 12) If the amount of gas in the cylinder in the previous question is mol and it has an initial temperature of 294 K. Calculate the final temperature of the gas in the cylinder. Assume that the process occurs too quickly for any heat to escape. 13)In coal-fired power plants, the water is boiled by the combustion of coal into highpressure steam. In a small plant, letʼs say the water vapour in the boiler has 5.0 MJ of thermal energy, if 4.0 MJ of heat is lost to the environment, how much work can be used to generate electrical energy? 14) What is the efficiency of the coal-fired power plant in the previous question? 15) If the temperature of the boiler in the coal-fired power plant in Question 12 is 420 K calculate the theoretical maximum efficiency if the outside temperature is a) 280 K b) 310 K c) Explain why it is harder for utility companies to meet customer demand for electricity on hotter days.

5 16) The following is a P-V graph showing the four thermodynamic processes which occur in a Carnot engine. Match the processes with the labels. Labels: Isothermic expansion Isothermic compression Adiabatic expansion Adiabatic compression 17) Explain how the work performed by the engine in the previous question could be calculated. 18) As a systemʼs entropy increases, how does its capacity to do work change? 19) For the following situations state whether the entropy increases or decreases. a) A balloon is inflated b) A balloon is allowed to deflate c) A deck of playing cards is shuffled d) A battery is recharged e) A battery is discharged f) A match burns g) The vapours from a stink bomb diffuse throughout a school h) The water cycle transports vast quantities of water from the oceans to the land 20) For each of the examples above, how does the total entropy of the universe change?