Grade 11 : Physics - Thermal Properties (Set 7)

Convert a temperature reading of $50^\circ\text{C}$ to the Fahrenheit and Kelvin scales.

A brass rod has a length of 2.0 m at $20^\circ\text{C}$. If the coefficient of linear expansion of brass is $\alpha = 2.0 \times 10^{-5}\text{ K}^{-1}$, calculate the increase in length when heated to $120^\circ\text{C}$.

For an isotropic solid material, what is the theoretical ratio between the coefficient of linear expansion ($\alpha$), coefficient of area expansion ($\beta$), and coefficient of volume expansion ($\gamma$)?

A steel rod of cross-sectional area $4.0 \times 10^{-4}m^2$ is rigidly clamped at both ends at $25^\circ\text{C}$. If Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$ and coefficient of linear expansion $\alpha = 1.2 \times 10^{-5}\text{ K}^{-1}$, find the tension developed in the rod when cooled to $5^\circ\text{C}$.

A pendulum clock made of steel ($\alpha = 1.2 \times 10^{-5}\text{ K}^{-1}$) keeps accurate time at $20^\circ\text{C}$. If the ambient temperature increases to $30^\circ\text{C}$, how much time does the clock gain or lose per day?

A container holds 100 g of ice at $0^\circ\text{C}$. If 100 g of liquid water at $80^\circ\text{C}$ is poured into it, what will be the final temperature of the mixture at thermal equilibrium? (Latent heat of fusion of ice $L_f = 80\text{ cal/g}$, specific heat of water $c = 1\text{ cal/(g}\cdot^\circ\text{C)}$)

A calorimeter of mass 100 g is made of a metal with specific heat capacity $0.10\text{ cal/(g}\cdot^\circ\text{C)}$. What is the water equivalent of this calorimeter?

Calculate the total heat required to convert 50 g of ice at $0^\circ\text{C}$ into steam at $100^\circ\text{C}$. ($L_f = 80\text{ cal/g}$, $c_{\text{water}} = 1\text{ cal/(g}\cdot^\circ\text{C)}$, $L_v = 540\text{ cal/g}$)

A composite wall is formed by two layers of equal thickness $d$ having thermal conductivities $K_1$ and $K_2$. What is the equivalent thermal conductivity $K_{eq}$ for steady heat flow perpendicular to the layers (in series)?

Two metal rods of equal length and equal cross-sectional area are connected in series as shown above. Their thermal conductivities are $300\text{ W/(m}\cdot\text{K)}$ and $100\text{ W/(m}\cdot\text{K)}$. If the open ends are kept at $100^\circ\text{C}$ and $0^\circ\text{C}$, what is the junction temperature $T_j$?

What is the dimensional formula for thermal conductivity ($K$)?

A black body at absolute temperature 300 K emits thermal energy at a rate of $E$. If its absolute temperature is increased to 600 K, what will be the new rate of thermal energy emission?

The wavelength corresponding to maximum spectral emissive power for a black body at 2000 K is $1.5\ \mum$. What will be the peak wavelength when its temperature is increased to 3000 K?

A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes in surroundings kept at $20^\circ\text{C}$. Using Newton's Law of Cooling, how long will it take to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ in the same surroundings?

At what temperature does pure water exhibit its maximum density at standard atmospheric pressure?

If a liquid of coefficient of real cubical expansion $\gamma_r$ is contained in a vessel of coefficient of cubical expansion $\gamma_v$, what is the coefficient of apparent expansion $\gamma_a$ of the liquid?

According to Kirchhoff's Law of thermal radiation, what is the ratio of emissive power ($E$) to absorptive power ($a$) for any body in thermal equilibrium?

What is the ratio of specific heat capacities $\gamma = C_p / C_v$ for an ideal monatomic gas?

A spherical black body of radius 10 cm at 500 K is suspended in an evacuated enclosure maintained at 300 K. Calculate the net rate of heat loss by radiation. (Use $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$, $\pi \approx 3.14$)

What is the ratio of the rate of heat conduction in Rod A to that in Rod B ($H_A : H_B$)?