(B) The heat energy $dQ$ required to raise the temperature of a unit mass $(m = 1)$ by a small amount $dT$ is given by $dQ = m \cdot S \cdot dT$.Subst

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(B) The heat energy $dQ$ required to raise the temperature of a unit mass $(m = 1)$ by a small amount $dT$ is given by $dQ = m \cdot S \cdot dT$.Substituting $S = aT^3$ and $m = 1$,we get $dQ = aT^3 \ dT$.To find the total heat energy $Q$ required to raise the temperature from $T_1 = 1 \ K$ to $T_2 = 2 \ K$,we integrate the expression:$Q = \int_{1}^{2} aT^3 \ dT$$Q = a \left[ \frac{T^4}{4} \right]_{1}^{2}$$Q = \frac{a}{4} (2^4 - 1^4)$$Q = \frac{a}{4} (16 - 1)$$Q = \frac{15 \ a}{4}$

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Heat Capacity, Specific Heat and Molar Specific Heat

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The specific heat of a metal at low temperatures varies according to $S = aT^3$,where $a$ is a constant and $T$ is the absolute temperature. The heat energy needed to raise unit mass of the metal from $T = 1 \ K$ to $T = 2 \ K$ is:

A
$3 \ a$
B
$\frac{15 \ a}{4}$
C
$\frac{2 \ a}{3}$
D
$\frac{12 \ a}{5}$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Heat Capacity, Specific Heat and Molar Specific Heat

The specific heat of a substance at temperature $T^{\circ}C$ is given by $C = \alpha T^2 + \beta T + \gamma$. The amount of heat required to raise the temperature of a mass $m \, g$ of the substance from $0^{\circ}C$ to $T_o^{\circ}C$ is .......

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How much energy in $kJ$ is required to heat $5 \, kg$ of water from $20^oC$ to its boiling point? (Specific heat of water = $4.2 \, kJ \, kg^{-1} \, ^oC^{-1}$)

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The specific heat of a metal at low temperatures varies according to $S = aT^3$,where $a$ is a constant and $T$ is the absolute temperature. The heat energy needed to raise unit mass of the metal from $T = 1 \ K$ to $T = 2 \ K$ is:

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The specific heat of a substance at temperature $T^{\circ}C$ is given by $C = \alpha T^2 + \beta T + \gamma$. The amount of heat required to raise the temperature of a mass $m \, g$ of the substance from $0^{\circ}C$ to $T_o^{\circ}C$ is .......

If the temperature scale is changed from $^\circ C$ to $^\circ F$, the numerical value of specific heat will

$A$ substance is cooled at a constant power. Its temperature vs time graph is shown. The value of $S_{solid} : S_{liquid} : S_{gas}$ is:

The heat required to increase the temperature of a body by $1^{\circ}C$ is called........

How much energy in $kJ$ is required to heat $5 \, kg$ of water from $20^oC$ to its boiling point? (Specific heat of water = $4.2 \, kJ \, kg^{-1} \, ^oC^{-1}$)

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