Thermal properties of matter practice · Mixed difficulty

Option D (${\mathrm{U}_2}\, > \,{\mathrm{U}_1}$) is correct because the wavelength of maximum emission shifts according to Wien's displacement law, and 500nm is closer to that wavelength than 250nm.

Option A (Expands while freezing) is correct because increasing pressure favors the phase with smaller volume. If a liquid expands upon freezing, increasing pressure will hinder the freezing process, thus decreasing the freezing point.

Option C (74.96 cm) is correct because it accounts for the thermal expansion of the brass scale in the barometer.

Option A (Conduction) is correct because convection requires gravity for fluid movement, and radiation is less efficient in liquids.

Option A ($70 \mathrm{~m}$) is correct because, under isothermal conditions, the product of pressure and volume is constant. Using this, the depth can be calculated.

Option D (Kelvin) is correct because the Kelvin scale starts at absolute zero (0 K) and only has positive values.

Option A (It absorbs energy) is correct because melting is an endothermic process, meaning it requires energy input to break the bonds holding the solid structure together.

Option B (2.8mm) is correct because the change in length is calculated by summing the expansions of both brass and steel rods.

Option C (Are bad conductors of heat) is correct because wool has low thermal conductivity, trapping air and reducing heat loss from the body.

Option C is correct. The assertion is true because thick glass is a poor conductor of heat, leading to uneven expansion and cracking. The reason is false because the inner surface expands first, not the outer.

Option C (1 gm) is correct because the rate of heat transfer depends on the ratio of area to length, which remains constant.

Option A ($2\;cal/K$) is correct because the value of R in calories is approximately 2 cal/K.

Option C (Only utensil will shine) is correct because the utensil, being black, will emit radiation due to its temperature, while the carving, being part of the utensil, will not independently shine.

Option A ($1$) is correct because a perfectly black body absorbs all incident radiation, meaning its absorptive power is 1.

Option A (${43^0}C$) is correct because it is the approximate temperature of the body after the next 10 minutes, calculated using Newton's law of cooling.

Option A (Coefficient of cubical expansion of liquid must be greater than that of bulb material) is correct because for a thermometer to function properly, the liquid must expand more than the bulb material when heated, allowing the liquid to rise in the tube.

Option C ($327^\circ C$) is correct because it is calculated using Charles's Law, relating volume and temperature at constant pressure.

Efficiency of carnot engine cannot be made larger than 50 % is the correct answer because if the efficiency is 40% with a source at 500K, then the sink temperature is 300K. With this sink temperature, an efficiency of 60% would require a source temperature of 750K. However, the problem states that 200 cal of heat is given, whose efficiency is 40 %, takes is heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60 % Then, the intake temperature for the same exhaust (sink). Temperature must be

Option B (3 s) is correct because when in parallel, the effective area doubles, leading to a fourfold increase in heat transfer rate and a quarter of the time.

Option B (Colour of the liquid) is correct because the apparent expansion of a liquid depends on the nature of the liquid, the change in temperature, and the material of the vessel, but not the color of the liquid.

Option A ($1425 \mathrm{~W}$) is correct because it is the radiation power calculated using Stefan-Boltzmann law with the given temperature, radius, and emissivity.

Option D ($l/KA$) is correct because thermal resistance is defined as the ratio of length to the product of thermal conductivity and area.

Option D (Water expands when cooled from $4^0 {C}$ to $0^{\circ} {C}$) is correct because water has a unique property of expanding when cooled from 4°C to 0°C, making the colder water less dense and rise to the top.

Option B (In cool air near the bottom and hot air out near the roof) is correct because hot air rises and exits through the top windows, while cool air enters through the bottom windows, creating a natural convection current.

Option B ($\frac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2}$) is correct because the effective conductivity is derived from the series combination of resistances.

Option D is correct. Absolute zero, which is 0 Kelvin, corresponds to -273.15°C on the Celsius scale.

Option B ($\frac{3}{{1.01}}$) is correct because it represents the mass of liquid expelled calculated using the densities and the coefficient of linear expansion.

Option B (White) is correct because as a black body is heated to high temperatures, it emits radiation across the visible spectrum, resulting in a white appearance.

Option B ($40^\circ C$) is correct because it is calculated using linear interpolation based on the resistance values at different temperatures.

Option C (Radiation) is correct because radiation does not require a medium for heat transfer and can occur at the speed of light, making it the fastest mode of heat transfer.