Gases

Question 1

What is the average kinetic energy of n moles of an ideal gas?

Answer 1

• 3/2nRT
• For a monoatomic gas, without internal bond vibrations, the change in internal energy is equal to the change in translational kinetic energy

Question 2

What is the relationship between R and the heat capacity of a gas at constant volume?

Answer 2

• The change in the internal energy of a monoatomic gas is 3/2nR ΔT
• In a constant volume setting, the change in the internal energy is just the heat put into the system, which equals nC_V ΔT
• If we cancel n and ΔT, we see that Cv = 3/2R

Question 3

What is the mathematical relationship between C_Vand C_P?

Answer 3

• C_Pis greater because some of the energy transfer is used to do work rather than increase the internal energy
• U = q + w; for a given change in temperature ΔT,
  
  • U = q_v = nc_v ΔT
  • q_p= nc_p ΔT, so
  • ncv ΔT = ncp ΔT + work, which equals ΔPV, which equals nRΔT
  • Cancel our n ΔT on all sides, find that
  • Cp = Cv + R
• So, for a monoatomic ideal gas, C_p= 5/2R

Question 4

What is happening at each of these steps?

Answer 4

• 1 to 2: Volume increase with constant pressure; gas must be heated
• 2 to 3: Constant volume, dropping pressure; temperature must be decreasing. Constant volume cooling
• 1 to 4: Pressure decreasing at constant volume; cooling
• 4 to 3: Heating at constant pressure

Remember, whenever pressure OR volume is changing (but not both) the temperature or number of moles must also be changing

Question 5

What is the heat of fusion?

Answer 5

The heat necessary to transform 1 mol of substance from solid to liquid

This is an endothermic process

The heat of freezing is the negative of this, and this process is exothermic

Question 6

What is the heat of vaporization?

Answer 6

This is the heat necessary to transform one mol into vapor phase

This is endothermic; negative of energy of condensation, which is an exothermic process

Question 7

What is the term for a constant volume reaction?

Answer 7

Isochoric

Question 8

What is the term for a constant pressure reaction?

Answer 8

Isobaric

Question 9

For an ideal, monoatomic gas, what parameter does the internal energy depend on?

Answer 9

The temperature

Question 10

What is the change in internal energy for an isothermal process?

Answer 10

Internal energy depends on temperature, so if the temperature remains constant, then so does the internal energy; work and heat must cancel each other out

Question 11

How do you calculate the work done on the system in an isothermal process?

Answer 11

• Pressure and volume are changing at the same time, so the total work done is the integral of pressure with respect to volume
• w = -(int)v1-v2 (PdV)
• Because PV = nRT, P = (nRT)(1/V), so we can rewrite the integral as nRT(int)v1-v2(1/V dv)
• Therefore, the formula for the work done in an isothermal process is:
  
  • -nRTln(V2/V1)

Question 12

What is an adiabatic process?

Answer 12

A process in which there is no transfer of heat into or out of the system

Therefore, the change in internal energy exactly equals the work done on the system

Question 13

What is the equation for calculating the work done on a system in an isothermal process?

Answer 13

w = -nRTln(V2/V1)

• In an expansion, negative work is being done on the system (the system is doing positive work), V2/V1 is positive and the work done on the system is negative

Question 14

What is the equation for calculating the heat transfer in an isothermal process?

Answer 14

q = nRTln(V2/V1)

The heat transferred to the system is exactly equal to the work done on the system, because there is no change in the internal energy of the system

In an expansion, heat enters the system to drive the work done by the system; in a compression, heat leaves the system to compensate for the work being done on the system

Question 15

For a given change in volume, does pressure decrease faster in an adiabatic or an isothermal process?

Answer 15

The pressure drops more quickly in an adiabatic process, because when the volume increases, the temperature drops, causing the pressure to decrease; for an isothermal process, the temperature remains the same, so the pressure only drops to compensate for the increase in volume