Heat Capacity of Ideal Gases and Adiabatic Compressions

Question 1

U for a Monoatomic Gas

Answer 1

𝑈 = 3/2𝑛𝑅*𝑇

Question 2

𝐶𝑉 and CP for a Monoatomic Gas and why

Answer 2

𝐶𝑉 = 3/2𝑛𝑅
𝐶𝑃 = 𝐶𝑉 + 𝑛𝑅 = 5/2𝑛𝑅

Cp = Cv + nR

Question 3

Degrees of Freedom in a Monoatomic Gas

Answer 3

3 - translational only

Question 4

Degrees of Freedom in a Diatomic Gas

Answer 4

5 (3 translational + 2 rotational)

Question 5

U in a Diatomic Gas

Answer 5

U = 5/2nRT

Question 6

Cp and Cv for a diatomic gas and why

Answer 6

CV = 5/2nR
𝐶𝑃 = 7/2𝑛𝑅

Cp = Cv + nR

Question 7

Degrees of Freedom in Triatomic Gas

Answer 7

7 (3 translational, 2 rotational, 2 vibrational)

Question 8

U in a Triatomic Gas

Answer 8

U = 7/2nRT

Question 9

Cv and Cp in a Triatomic Gas and why

Answer 9

CV = 7/2nR,
𝐶𝑃 = 9/2𝑛𝑅

CP = Cv + nR

Question 10

What is the First Law for adiabatic processes?

Answer 10

ΔU=W, because 𝑄 = 0

Question 11

What is the adiabatic condition for pressure and volume?

Answer 11

PV^γ = constant

Question 12

What is the adiabatic condition for temperature and volume?

Answer 12

TV^γ−1 = constant

Question 13

What is the adiabatic condition for pressure and temperature?

Answer 13

T^γ^ * P^1−γ =constant

Question 14

What is the adiabatic index 𝛾 for monoatomic gases?

Answer 14

γ = 5/3​

Question 15

What is 𝛾 for diatomic gases?

Answer 15

γ = 7/5

Question 16

What does 𝛾 equal in terms of heat capacities?

Answer 16

𝛾 = 𝐶𝑃/𝐶𝑉

Question 17

What is the key condition in isothermal compression?

Answer 17

ΔT=0 → Δ𝑈 = 0, so Q =−W

Question 18

What is the key condition in adiabatic compression?

Answer 18

Q=0 → Δ𝑈 = 𝑊

Question 19

Which compression type performs more work: isothermal or adiabatic?

Answer 19

Adiabatic → greater pressure change for same volume

Question 20

Relationship between change in U and change in T

Answer 20

ΔU = CV * ΔT