Thermal properties of matter practice · Mixed difficulty

Option B (${\frac{{{K_1} + {K_2}}}{2}}$) is correct because it represents the equivalent thermal conductivity for two layers in parallel with equal thickness.

Option Yellow is incorrect. As temperature increases, the color shifts from red to orange to yellow to white to blue. Therefore, the color will become white.

Option A (18 gram) is correct because the water equivalent is calculated by multiplying the mass of the copper block by its specific heat.

Option B ($600^\circ C$) is correct because it is the temperature increase calculated using the formula for linear thermal expansion.

Option C (If Assertion is true, but the Reason is false) is correct because the rate of melting increases four times, but the thermal resistance decreases to one-fourth.

Option A (If both (A) and (R) are true and (R) is the correct explanation of (A)) is correct because water expands upon freezing due to its anomalous expansion, causing pipes to burst.

Option A (Conduction) is correct because conduction is the transmission of heat through a material by molecular collisions.

Option C (Volume increases and density decreases) is correct because as temperature increases, liquids expand (increasing volume) and density decreases (since density = mass/volume).

Option B (${40^0}C$) is correct because it is calculated directly from the heat flow equation, using the given values for heat flow rate, thermal conductivity, area, and length.

Option A (2.43) is incorrect. Option B (3.43) is incorrect. Option C (4.45) is incorrect. Option D (5.43) is incorrect. There appears to be an error in the provided solution. The correct answer should be 3.43. The provided solution calculates the equivalent resistance incorrectly, leading to an incorrect thermal conductivity. The correct approach involves using the formula for equivalent thermal conductivity for rods in series: $\frac{L}{K_{eq}A} = \frac{L_1}{K_1A} + \frac{L_2}{K_2A}$. Since $L_1 = L_2 = L/2$, we have $\frac{L}{K_{eq}A} = \frac{L/2}{3A} + \frac{L/2}{4A}$, which simplifies to $\frac{1}{K_{eq}} = \frac{1}{6} + \frac{1}{8} = \frac{4+3}{24} = \frac{7}{24}$. Thus, $K_{eq} = \frac{24}{7} \approx 3.43$.

Option A (The spot will appear brighter than the plate) is correct because according to Kirchhoff's law, good absorbers are good emitters, and the black spot is a good absorber.

Option A (Wavelength corresponding to maximum energy and temperature) is correct because Wien's displacement law states that the wavelength at which the black body emission spectrum is at a maximum is inversely proportional to the absolute temperature.

Option B is correct because saturated water vapor does not obey ideal gas laws, and during isothermal compression, the pressure remains constant until all vapor condenses.

Option B (Thermal capacity) is correct because thermal capacity is the amount of heat required to raise the temperature of a substance by 1 degree Celsius.

Option C (Assertion (A) is true, Reason (R) is false) is correct because a 2% increase in length leads to a 6% increase in volume, but the coefficient of volume expansion is three times the linear expansion, not two.

Option A ($41.84\,\frac{J}{K}$) is correct because it is the thermal capacitance calculated by multiplying mass and specific heat capacity, then converting to Joules.

Option C (${4^0}C$) is correct because water has maximum density at ${4^0}C$, so the bottom of the lake will be at this temperature.

Option B ($P$) is correct because the isothermal bulk modulus of an ideal gas is equal to its pressure.

Option C is correct because the focal length changes sign and magnitude when immersed in a liquid with a higher refractive index.

Option B is correct because while both the assertion and reason are true, the high thermal conductivity of water is not the primary reason for moderate temperatures near the sea coast; it's due to water's high specific heat and convection currents.

Option A (Only the block is heated) is correct because steel has a higher coefficient of expansion than bronze, so heating the steel block expands the hole more efficiently.

Option B (Low specific heat and high thermal conductivity) is correct because a cooking pot should heat up quickly (low specific heat) and transfer heat efficiently to the food (high thermal conductivity).

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

Option A ($\frac{1}{2} \lambda_m$) is correct because it is the wavelength calculated using Wien's displacement law, which states that the product of the peak wavelength and temperature is constant.

The correct answer is C ($P V$) because dimensional analysis of the van der Waals equation reveals that a/b has the same dimensions as PV.

Option A (1) is correct because the rate of heat flow is directly proportional to thermal conductivity and area, and inversely proportional to length. Considering the ratios, the heat flow in the shorter rod is 1 cal/s.

Option B (2.4) is correct because the equivalent thermal conductivity is calculated using the formula for series combination of thermal resistances.

Option B is correct because low thermal conductivity prevents heat from quickly reaching the hand, and high specific heat means the pan handle heats up slowly.

Option C (Radiation) is correct because radiation involves the transfer of heat through electromagnetic waves, which can travel through a vacuum and is therefore the fastest mode of heat transfer.

Option B ($320 {~W}$) is correct because the radiating power is proportional to the difference of the fourth power of the temperatures of the black body and its surroundings.