Grade 11 : Physics - Thermal Properties (Set 8)

At what temperature do the Celsius and Fahrenheit temperature scales yield numerically equal values?

A brass rod of initial length 1.5 m at $20^\circ\text{C}$ is heated to $70^\circ\text{C}$. What is the increase in its length?

A thin copper plate of area $0.5m^2$ at $10^\circ\text{C}$ is heated to $110^\circ\text{C}$. If the coefficient of linear expansion is $\alpha = 1.7 \times 10^{-5}\text{ K}^{-1}$, what is the increase in surface area?

A steel rod is rigidly clamped at both ends at $30^\circ\text{C}$. If the temperature drops to $10^\circ\text{C}$, find the thermal stress set up in the rod. (Young's modulus $Y = 2 \times 10^{11}\text{ N/m}^2$, $\alpha = 1.2 \times 10^{-5}\text{ K}^{-1}$)

How much thermal energy is required to raise the temperature of 2 kg of aluminum from $25^\circ\text{C}$ to $75^\circ\text{C}$? (Specific heat capacity $c = 900\text{ J/(kg}\cdot\text{K)}$)

A mass of 0.2 kg of water at $80^\circ\text{C}$ is mixed with 0.3 kg of water at $20^\circ\text{C}$ in an insulated container. What is the final equilibrium temperature?

Calculate the heat energy required to completely melt 0.5 kg of ice at $0^\circ\text{C}$ into liquid water at $0^\circ\text{C}$. (Latent heat of fusion $L_f = 3.36 \times 10^5\text{ J/kg}$)

A glass window of surface area $1.2m^2$ and thickness 4 mm separates indoor air at $20^\circ\text{C}$ from outdoor air at $5^\circ\text{C}$. Thermal conductivity of glass is $0.8\text{ W/(m}\cdot\text{K)}$. Find the rate of heat transfer through the window.

Two metallic slabs of equal thickness $L$ and equal cross-sectional area $A$ have thermal conductivities $k_1 = 100\text{ W/(m}\cdot\text{K)}$ and $k_2 = 300\text{ W/(m}\cdot\text{K)}$. If they are connected in series, what is the equivalent thermal conductivity of the combination?

A blackbody at absolute temperature 300 K radiates energy at a rate $E$. If its temperature is increased to 600 K, what is the new rate of energy radiation?

The peak wavelength corresponding to maximum spectral radiance of a black body at 2900 K is $1.0\,\mum$. What will be the peak wavelength if the body cools to 1450 K?

Using Newton's law of cooling, how long will it take for the same body to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ in the same room?

A liquid has a coefficient of real volume expansion $\gamma_{real} = 7 \times 10^{-4}\text{ K}^{-1}$. It is heated inside a metal vessel with linear expansion coefficient $\alpha = 1 \times 10^{-5}\text{ K}^{-1}$. What is the coefficient of apparent volume expansion of the liquid?

When liquid water is heated from $0^\circ\text{C}$ to $4^\circ\text{C}$, what happens to its volume and density?

For an ideal gas, the molar heat capacity at constant pressure is $C_p = \frac{7}{2}R$. What is the ratio of specific heats $\gamma = \frac{C_p}{C_v}$ for this gas?

Two identical metallic rods each having thermal resistance $R_0 = 10\text{ K/W}$ are connected in parallel between two heat reservoirs. What is the net thermal resistance of the combination?

The time required for an ice layer on a frozen pond to grow from 0 cm to 2 cm thickness is $t_1$. How long $t$ will it take for the thickness to increase from 2 cm to 4 cm under constant freezing air temperature?

The Sun has radius $R$ and surface temperature $T$. What is the intensity of solar radiation incident on Earth located at a mean orbital distance $d$ from the Sun's center?

A solid cube of edge length 10 cm at $20^\circ\text{C}$ is heated to $120^\circ\text{C}$. If linear expansion coefficient $\alpha = 2 \times 10^{-5}\text{ K}^{-1}$, what is the increase in volume of the cube?

Steam at $100^\circ\text{C}$ is passed into 0.1 kg of water at $20^\circ\text{C}$. How much steam must condense to raise the water temperature to $100^\circ\text{C}$? ($c_{\text{water}} = 4200\text{ J/(kg}\cdot\text{K)}$, $L_v = 2.26 \times 10^6\text{ J/kg}$)