Heat and Thermodynamics — NDA Physics

Formulas (3)

• Temperature and the three scales · Temperature-scale conversions
  $$\frac{C}{5} = \frac{F - 32}{9} = \frac{K - 273.15}{5} \qquad F = \frac{9}{5}C + 32 \qquad K = C + 273.15$$
• Thermal expansion — linear, areal, and volume coefficients · Expansion coefficients are in the ratio 1 : 2 : 3
  $$\Delta L = L\alpha\,\Delta\theta \qquad \beta = 2\alpha \qquad \gamma = 3\alpha = \tfrac{3}{2}\beta$$
• Consequences of expansion — pendulums and liquid measurement · Pendulum period and apparent expansion
  $$T = 2\pi\sqrt{\frac{L}{g}} \qquad \frac{\Delta T}{T} = \frac{1}{2}\alpha\,\Delta\theta \qquad \gamma_{\text{real}} = \gamma_{\text{apparent}} + \gamma_{\text{vessel}}$$

Watch out for (6)

• A temperature CHANGE is the same in K and °C, but a temperature VALUE is not
  → Temperature and the three scales
• Never write a degree sign with Kelvin
  → Temperature and the three scales
• Absolute zero is −273°C, not −273 K
  → Absolute zero and choosing a thermometer
• Set the SCALE VARIABLES equal, not the formula sides
  → When do two scales read the same?
• Areal to volume is ×3/2, not ×3
  → Thermal expansion — linear, areal, and volume coefficients
• Heated pendulum slows DOWN — the period goes UP
  → Consequences of expansion — pendulums and liquid measurement

Formulas (3)

• Specific heat, thermal capacity, and Q = mcΔT · Sensible heat (no phase change)
  $$Q = mc\,\Delta\theta \qquad \text{Thermal capacity} = mc$$
• Latent heat and the calorimetry mixing balance · Latent heat + the mixing balance
  $$Q = mL \qquad \sum Q_{\text{lost}} = \sum Q_{\text{gained}}$$
• When specific heat varies with temperature · Heat for a temperature-dependent specific heat
  $$Q = m\int_{T_1}^{T_2}\!\big(C_0 + \alpha T\big)\,dT = m(T_2 - T_1)\left[C_0 + \tfrac{1}{2}\alpha(T_1 + T_2)\right]$$

Reference tables (1)

Watch out for (8)

• A body has internal energy, not 'heat'
  → Heat — energy in transit due to a temperature difference
• Specific heat is intrinsic; thermal capacity is not
  → Specific heat, thermal capacity, and Q = mcΔT
• Watch the units — kJ vs J, kg vs g
  → Specific heat, thermal capacity, and Q = mcΔT
• Don't forget the latent-heat term while ice is melting
  → Latent heat and the calorimetry mixing balance
• Keep masses in consistent units across both sides
  → Latent heat and the calorimetry mixing balance
• The factor on $\alpha$ is one-half, not one
  → When specific heat varies with temperature
• Only radiation crosses a vacuum
  → The three modes of heat transfer — conduction, convection, radiation
• A thermos REFLECTS radiation — it does not absorb it
  → The three modes of heat transfer — conduction, convection, radiation

Formulas (3)

• Latent heat of fusion and vaporization · Latent heat
  $$Q = mL$$
• Boiling point depends on pressure · Boiling condition
  $$P_{\text{vapour}} = P_{\text{atmospheric}}$$
• Newton's law of cooling · Newton's law of cooling
  $$-\frac{d\theta}{dt} \propto (\theta - \theta_0)$$

Watch out for (4)

• Latent heat is absorbed at CONSTANT temperature
  → Latent heat of fusion and vaporization
• Boiling is vapour pressure = atmospheric, not 'less than'
  → Boiling point depends on pressure
• Evaporation happens at ALL temperatures; boiling does not
  → Evaporation versus boiling
• Newton's law does NOT apply to phase changes or furnace heat
  → Newton's law of cooling

Formulas (3)

• The ideal gas law · Ideal gas law and the combined gas law
  $$PV = nRT \qquad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
• First law of thermodynamics · First law of thermodynamics
  $$\Delta U = Q - W$$
• Named processes — isothermal, adiabatic, isochoric, isobaric · Identify a process by substituting PV = nRT
  $$P = kT \;\Rightarrow\; V = \frac{nR}{k} = \text{const} \;\Rightarrow\; \text{isochoric},\; C = C_V$$

Reference tables (1)

Watch out for (5)

• Temperature in the gas law is ALWAYS in kelvin
  → The ideal gas law
• Internal energy of an ideal gas depends only on temperature
  → First law of thermodynamics
• Don't guess the process — substitute PV = nRT
  → Named processes — isothermal, adiabatic, isochoric, isobaric
• Adiabatic means no HEAT exchange, not no temperature change
  → Named processes — isothermal, adiabatic, isochoric, isobaric
• First law = energy; second law = direction
  → The second law and a process summary table