Thermal properties of matter practice · Mixed difficulty

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 A ($0.033^\circ \\,{C^{ - 1}}$) is correct because the temperature coefficient of resistance is calculated using the given resistance values at different temperatures.

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 B (In cool air near the bottom and hot air out near the roof) is correct because hot air rises and cool air sinks, creating a natural convection current.

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.

Option C (Volume and pressure of a gas becomes zero) is correct because, theoretically, at absolute zero, molecular motion ceases, leading to zero volume and pressure.

Option B is correct because the specific heat capacity is a property of the material itself and does not depend on the amount of heat given to the body.

Option A ($\frac{{{f_1} - {f_2}}}{{{f_2}{t_1} - {f_1}{t_2}}}$) is correct because it correctly represents the coefficient of volume expansion derived from Archimedes' principle and density variations with temperature.

Option B ($45^\circ$) is correct because the angle of friction is the arctangent of the coefficient of friction, and arctan(1) = 45 degrees.

Option D (0.6) is correct because it is the specific heat of alcohol calculated using calorimetry principles.

Option D (Brass has a higher coefficient of linear expansion than iron) is correct because brass expands more than iron for the same temperature increase, causing the bimetallic strip to bend with brass on the convex side.