1st Law of TD and Heat Capacity

Question 1

What is internal energy (U)?

Answer 1

The total kinetic and potential energy of atoms/molecules in a system.

Question 2

What types of kinetic energy contribute to U in gases?

Answer 2

Translational, rotational, and vibrational energy.

Question 3

What is the KE contribution of each quadratic degree of freedom?

Answer 3

1/2 * 𝑘𝐵 * 𝑇

Question 4

What determines the internal energy of solids?

Answer 4

Vibrational kinetic energy and potential energy of interatomic bonds.

Question 5

Is internal energy path-dependent?

Answer 5

No, ΔU is a state function and path-independent.

Question 6

KE for translational motion of molecules

Answer 6

KE = 1/2mv^2 = 1/2m(vx^2 + vy^2 + vz^2)

Question 7

KE for rotational motion of molecules

Answer 7

KE = 1/2 I w^2

w = angular velocity

I = moment of inertia`

Question 8

What does the First Law of Thermodynamics state?

Answer 8

ΔU=Q+W

Question 9

In an adiabatic process, what is
𝑄?

Answer 9

Q=0; no heat transfer → Δ𝑈 = 𝑊

Question 10

What does it mean for a system to be adiabatic vs. diathermal?

Answer 10

Adiabatic: no heat exchange. Diathermal: allows heat exchange.

Question 11

Can work be done in an adiabatic process?

Answer 11

Yes — it results in a change in internal energy.

Question 12

What does it mean when Δ𝑈 =0?

Answer 12

The system returns to its initial state; 𝑄 = −𝑊

Question 13

Define heat in thermodynamics.

Answer 13

Non-mechanical energy transfer due to a temperature difference.

Question 14

What are the three mechanisms of heat transfer?

Answer 14

Conduction, convection, and radiation.

Question 15

What is the Stefan-Boltzmann Law?

Answer 15

P=σϵAT^4, where 𝜎 is the Stefan-Boltzmann constant.

Question 16

How does heat flow?

Answer 16

Spontaneously from higher to lower temperature.

Question 17

What does Planck’s distribution law say about peak wavelength?

Answer 17

λ max ∝ 1/T

Question 18

Formula for conduction

Answer 18

Q/t = Kt * A * (Th - Tc) / L

Question 19

Formula for Radiatiomn

Answer 19

P=σϵAT ^4

Question 20

Define heat capacity (C).

Answer 20

C= dQ / dT
​
; heat required to change temperature by 1 K.

Question 21

Define specific and molar heat capacities.

Answer 21

𝐶 sp = 1/m * 𝑑𝑄/𝑑𝑇

C mol = 1/n * dQ/dt
​

Question 22

How is enthalpy defined?

Answer 22

𝐻 = 𝑈 + 𝑃𝑉

Question 23

In an isochoric process, what does 𝐶𝑉 represent?

Answer 23

CV =(∂U / ∂T) V

Question 24

In an isobaric process, what does 𝐶𝑃 represent?

Answer 24

CP =( ∂H / ∂T ) P

Question 25

When is Δ𝐻 =𝑄

Answer 25

In processes at constant pressure