The First Law of Thermodynamics Ideal Gas Processes 11.4, 12.3

PV Diagrams Each point on a PV diagram represents a single, unique state of a gas. Consider the diagram shown here for 1 mol of a gas.

Ideal Gas Processes If a container is sealed, what can you say about the number of moles (and molecules) of a gas in the container? What does this mean for the ideal gas law?

Internal Energy We already know that internal energy is related to the temperature of the gas. There are two ways to change the amount of energy that a gas has. Q: If the gas in your system has a different temperature than its environment (surroundings), energy can be transferred (added or removed) as heat through conduction, convection, or radiation. W: Doing work on a system is also a way to change the energy of the system.

The First Law of Thermodynamics How will a change in energy manifest itself? What’s the difference between work done on a gas and work done by a gas?

A system absorbs 200 J of heat energy from the environment and does 100 J of work on the environment. What is its change in internal energy?

How much work does the environment do on a system if its internal energy changes from 40,000 J to 45,000 J without the addition of heat?

How would you find the work done on a gas from a graph?

Calculate the work done on a gas that expands from 0. 020 m3 to 0 Calculate the work done on a gas that expands from 0.020 m3 to 0.80 m3 at constant atmospheric pressure. How much work is done by the gas when the gas expands this much?

A cylinder with a moveable piston contains 0. 016 mol of helium A cylinder with a moveable piston contains 0.016 mol of helium. A researcher expands the gas via the process illustrated in the PV diagram. (a) Did the temperature of the gas increase, decrease, or remain constant? How do you know? (b) What is the change in internal energy of the gas? (c) How much work is done on the gas? (d) To achieve this change, does the researcher need to heat the gas? If so, how much heat must be added or removed?

The temperature of three moles of a monatomic ideal gas can be reduced from Ti = 540 K to Tf = 350 K by two different methods. In the first method 5500 J of heat flows into the gas, while in the second, 1500 J of heat flows into it. In each case, find (a) the change in internal energy, (b) the work done by the gas, and (c) sketch a PV diagram of the process.

Isovolumetric Processes

Isobaric Processes P V

What is the change in volume of a cylinder operating at atmospheric pressure if its internal energy decreases by 230 J when 120 J of heat are removed from it?

Isothermal Processes P V How could you make an isothermal process occur?   Why does the speed at which this process occurs matter?

Adiabatic Processes P V How could you make an adiabatic process occur?   Why does the speed at which this process occurs matter? P V

Practice Problems For each problem: Sketch a PV diagram of the process. Fill in the table for each problem. You do not need to do any calculations.

A snorkeler takes a deep breath at the surface, filling his lungs with 4.0 L of air. He then descends to a depth of 5.0 m, where the pressure is 0.50 atm higher than at the surface. At this depth, what is the volume of air in the snorkeler's lungs? Type of Process ΔT ( +, - , 0 ) ΔU Q W   P V

A gas in a cylinder with a moveable piston occupies 50. 0 cm3 at 50°C A gas in a cylinder with a moveable piston occupies 50.0 cm3 at 50°C. The gas is cooled at constant pressure until the temperature is 10°C. What is the final volume? Type of Process ΔT ( +, - , 0 ) ΔU Q W   P V

The pressure in a car tire is 30 The pressure in a car tire is 30.0 psi on a cool morning when the air temperature is 0° C. After the day warms up and bright sun shines on the black tire, the temperature of the air inside the tire reaches 30°C. What is the tire pressure at this temperature? Type of Process ΔT ( +, - , 0 ) ΔU Q W   P V