Thermal properties of matter practice · Medium

Option D is correct because the process follows PT = constant, which represents a hyperbola on the P-T diagram.

Option D ($\frac{\mathrm{x}_1}{\mathrm{~K}_1}+\frac{\mathrm{x}_2}{\mathrm{~K}_2}+\frac{\mathrm{x}_3}{\mathrm{~K}_3}=\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{\mathrm{~K}}$) is correct because the thermal resistances add in series, and the equivalent thermal resistance is the sum of individual resistances.

Option B (22000 N) is correct because the force exerted against the supports is calculated using the formula $F = YA\alpha \Delta t$, where Y is Young's modulus, A is the cross-sectional area, $\alpha$ is the coefficient of linear expansion, and $\Delta t$ is the change in temperature.

Option B (Same in both balloons) is correct because, according to the ideal gas law, at the same pressure and temperature, equal volumes contain the same number of molecules, regardless of the gas.

Option C (If (A) is true but (R) is false) is correct because pressure increases with temperature due to increased molecular collisions, not decreased.

Option B (Positive work is done on the ice-water system by the atmosphere) is correct because ice has a lower density than water, so when it melts, the volume decreases, and the atmosphere does positive work on the system.

Option D (${\left( {300} \right)^4}$) is correct because the energy emitted by a black body is proportional to the fourth power of its absolute temperature (Stefan-Boltzmann Law).

Option C ($\frac{{kA}\left({T}_1-{T}_2\right)}{{L}}$) is correct because it represents the rate of heat transfer through a rod in steady state according to Fourier's law of heat conduction.

Option A is correct because 1 calorie is defined as the heat required to raise the temperature of 1 g of water from ${14.5^0}C$ to ${15.5^0}C$ at 760 mm of Hg.

Option D (36 times) is correct because the power radiated is proportional to the area and the fourth power of the temperature, resulting in a 36-fold increase.

Option C (If assertion is true, but reason is false) is correct because perspiration cools the body through evaporation, not by enhancing emissivity.

Option B (If both (A) and (R) are true but (R) is not the correct explanation of (A)) is correct because while both the assertion and reason are true, the reason doesn't directly explain why a constant volume gas thermometer should be filled at high temperature and low pressure.

Option B (Lower temperature) is correct because the boiling point of water decreases as the pressure is reduced.

Option D (Statement I is false; Statement II is true) is correct because water expands when cooled or heated from 4°C, and its density is maximum at 4°C.

Option A is correct because when a metallic plate is heated, it expands radially outwards, causing the hole to increase in size.

Option B (102 cm) is correct because the length of the aluminum rod is calculated by equating the increase in length of both rods, considering their respective coefficients of linear expansion.

Option C ($e_\lambda=a_\lambda$) is correct because, according to Kirchhoff's law, at a given temperature, the emissive power and absorptive power of a body are equal.

Option A ($25^\circ C,\,\,\alpha = 1.85 \times {10^{ - 5}}/^\circ C$) is correct because it satisfies the conditions where the clock shows correct time and the calculated coefficient of linear expansion.

Option B is correct because both the assertion and the reason are true, but the reason does not explain the assertion. Absolute zero is indeed -273.15°C, and the Kelvin and Celsius scales have the same degree size, but the latter doesn't explain the former.

Option A (radiation) is correct because the calorimeter loses heat to the surroundings primarily through radiation due to its surface exposure.

Option A ($1: 16$) is correct because the area under the black body spectrum curve is proportional to the fourth power of the temperature, according to Stefan-Boltzmann law.

Option C (If A is true but R is false) is correct because it is hotter over the top of a fire due to convection, not conduction.

Option C ($\frac{K}{L^2}=$ constant) is correct because, according to Ingen-Hauz's experiment, the thermal conductivity is proportional to the square of the length up to which the wax melts.

Option C (Temperature) is correct because the color of a star is directly related to its surface temperature, as described by Wien's displacement law.

Option D is correct. A heated piece of green glass in darkness will not be visible because it will primarily emit infrared radiation, which is invisible to the human eye.

Option B (${10^3}$) is correct because it represents the conversion factor from the MKS unit of Stefan's constant to the CGS unit.

Option D (${10^{18}}$ cal) is correct because it is calculated using the formula for heat loss considering the temperature gradient, conductivity, and earth's surface area.

Option A is correct because Kirchhoff's law states that a good radiator is also a good absorber at a given wavelength.

Option C (Unity) is correct because a perfect black body absorbs all incident radiation, and its emissivity is defined as 1.

Option B (Wien’s displacement law) is correct because it relates the peak wavelength of emitted radiation to the temperature of a black body, like a star.