1.State the relationship between Celsius, Fahrenheit, and Kelvin temperature scales.
Sol: $\frac{C}{5} = \frac{F - 32}{9} = \frac{K - 273.15}{5}$.
2.Define coefficients of linear, superficial, and cubical expansion ($\alpha, \beta, \gamma$).
Sol: $\alpha = \frac{\Delta L}{L \Delta T}$, $\beta = \frac{\Delta A}{A \Delta T}$, $\gamma = \frac{\Delta V}{V \Delta T}$. Ratio $\alpha : \beta : \gamma = 1 : 2 : 3$.
3.State Newton's Law of Cooling.
Sol: Rate of loss of heat is directly proportional to temperature difference between body and surroundings: $\frac{dQ}{dt} = -k(T - T_0)$.
4.State Stefan-Boltzmann Law for blackbody radiation.
Sol: Total emissive power of blackbody: $E = \sigma T^4$, where $\sigma = 5.67 \times 10^{-8} \text{ W/m}^2\text{K}^4$.
5.An iron rod of length $50 \text{ cm}$ is heated from $20^\circ\text{C}$ to $100^\circ\text{C}$. Find change in length ($\alpha = 1.2 \times 10^{-5} /\text{K}$).
Sol: $\Delta L = L \alpha \Delta T = 0.5 \times (1.2 \times 10^{-5}) \times 80 = 4.8 \times 10^{-4} \text{ m} = 0.48 \text{ mm}$.
6.Calculate heat required to convert $100 \text{ g}$ of ice at $0^\circ\text{C}$ to steam at $100^\circ\text{C}$ ($L_f = 80 \text{ cal/g}, c=1, L_v = 540 \text{ cal/g}$).
Sol: $Q = m L_f + m c \Delta T + m L_v = 100(80) + 100(1)(100) + 100(540) = 8000 + 10000 + 54000 = 72000 \text{ cal} = 72 \text{ kcal}$.
7.A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in $5 \text{ min}$ in surroundings at $20^\circ\text{C}$. Find time to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$.
Sol: $\frac{80-60}{5} = K(70 - 20) \implies 4 = 50 K \implies K = 0.08$. Next step: $\frac{60-40}{t} = 0.08(50-20) \implies \frac{20}{t} = 2.4 \implies t = 8.33 \text{ minutes}$.
8.Find thermal current through a copper rod of length $0.5 \text{ m}$ and cross-section $10 \text{ cm}^2$ held between $100^\circ\text{C}$ and $0^\circ\text{C}$ ($K = 400 \text{ W/m}\cdot\text{K}$).
Sol: $H = \frac{K A (T_1 - T_2)}{L} = \frac{400 \times 10^{-3} \times 100}{0.5} = 80 \text{ Watts}$.
