Thermal Properties of Matter — JEE Mains Physics

Formulas (3)

• Converting between linear temperature scales · Two linear scales
  $$\frac{X - X_{ice}}{X_{steam} - X_{ice}} = \frac{C}{100} = \frac{F - 32}{180} = \frac{K - 273}{100}$$
• Linear, area and volume expansion of solids and gases · Thermal expansion
  $$\Delta L = L\alpha\Delta T \qquad \Delta A = A(2\alpha)\Delta T \qquad \Delta V = V(3\alpha)\Delta T \qquad \gamma_{gas} = \frac{1}{V}\frac{dV}{dT}$$
• Thermal stress in a rod that cannot expand · Thermal stress
  $$\sigma = Y\alpha\Delta T \qquad F = YA\alpha\Delta T \qquad u = \tfrac{1}{2}Y(\alpha\Delta T)^{2}$$

Watch out for (7)

• Adding 32 to a temperature change
  → Converting between linear temperature scales
• Using 0 and 100 for a faulty thermometer
  → Converting between linear temperature scales
• Using α for an area or a volume
  → Linear, area and volume expansion of solids and gases
• Thinking a hole shrinks when the plate is heated
  → Linear, area and volume expansion of solids and gases
• Reporting the rise instead of the final temperature
  → Linear, area and volume expansion of solids and gases
• Measuring the temperature change from the wrong state
  → Thermal stress in a rod that cannot expand
• Putting the length into the force
  → Thermal stress in a rod that cannot expand

Formulas (3)

• Heat from a heater, a fuel or lost kinetic energy · Energy into heat
  $$Q = ms\Delta T \qquad \eta Pt = ms\Delta T \qquad f\cdot\tfrac{1}{2}mv^{2} = ms\Delta T + mL$$
• Latent heat and the heating curve · Latent heat and heating-curve slope
  $$Q = mL \qquad \frac{dT}{dQ} = \frac{1}{ms}$$
• Mixing ice and water: heat lost equals heat gained · Heat balance
  $$m_ws_w(T_w - T) = m_is_i(0 - T_i) + m_iL + m_is_w(T - 0)$$

Watch out for (8)

• Grams and kilograms in one equation
  → Heat from a heater, a fuel or lost kinetic energy
• Stopping at the melting point
  → Heat from a heater, a fuel or lost kinetic energy
• Which g the options use
  → Heat from a heater, a fuel or lost kinetic energy
• Temperature does not rise during melting
  → Latent heat and the heating curve
• Forgetting to warm the ice to 0°C first
  → Latent heat and the heating curve
• Latent heat in kJ
  → Latent heat and the heating curve
• Assuming all the ice melts
  → Mixing ice and water: heat lost equals heat gained
• Forgetting that melted ice also warms
  → Mixing ice and water: heat lost equals heat gained

Formulas (2)

• Slabs and rods in series: thermal resistance and junction temperature · Conduction in series
  $$H = \frac{KA\Delta T}{L} \qquad R = \frac{L}{KA} \qquad \theta = \frac{\theta_1R_2 + \theta_2R_1}{R_1 + R_2} \qquad K_{eq} = \frac{L_1 + L_2}{L_1/K_1 + L_2/K_2}$$
• Parallel paths, junctions, box walls and spherical shells · Parallel paths, junctions and shells
  $$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \qquad \sum \frac{\theta_i - \theta}{R_i} = 0 \qquad \frac{dm}{dt} = \frac{H}{L_f} \qquad R_{shell} = \frac{r_2 - r_1}{4\pi Kr_1r_2}$$

Watch out for (5)

• Adding conductivities in series
  → Slabs and rods in series: thermal resistance and junction temperature
• Forgetting that the area goes as r²
  → Slabs and rods in series: thermal resistance and junction temperature
• Using one face of a box
  → Parallel paths, junctions, box walls and spherical shells
• Treating a spherical shell as a flat slab
  → Parallel paths, junctions, box walls and spherical shells
• Losing the sign at a junction
  → Parallel paths, junctions, box walls and spherical shells

Formulas (1)

• Stefan's law, Wien's law and Newton's law of cooling · Radiation and cooling
  $$P = e\sigma AT^{4} \qquad \lambda_mT = b \qquad \frac{T_1 - T_2}{t} = k\left(\frac{T_1 + T_2}{2} - T_s\right) \qquad T - T_s = (T_0 - T_s)e^{-kt}$$

Watch out for (4)

• Celsius in Stefan's law
  → Stefan's law, Wien's law and Newton's law of cooling
• Averaging the wrong quantity
  → Stefan's law, Wien's law and Newton's law of cooling
• Minutes and seconds
  → Stefan's law, Wien's law and Newton's law of cooling
• Doubling the excess does not quadruple the rate
  → Stefan's law, Wien's law and Newton's law of cooling