(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

Medium

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

Subtopic

Heat Capacity, Specific Heat and Molar Specific Heat

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

DifficultAP EAMCET 2001

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The thermal capacity of $100 \,g$ of aluminum (specific heat $= 0.2 \,cal / g ^{\circ} C$) is ............ $cal / ^{\circ} C$.

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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 temperature of $5$ moles of a gas at constant volume is changed from $100^{\circ} C$ to $120^{\circ} C$. The change in internal energy is $80 \,J$. The total heat capacity of the gas at constant volume in $J/K$ is:

EasyTS EAMCET 2003

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Which of the following substances has the maximum specific heat capacity?

Easy

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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:

Similar Questions

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

The thermal capacity of $100 \,g$ of aluminum (specific heat $= 0.2 \,cal / g ^{\circ} C$) is ............ $cal / ^{\circ} C$.

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

The temperature of $5$ moles of a gas at constant volume is changed from $100^{\circ} C$ to $120^{\circ} C$. The change in internal energy is $80 \,J$. The total heat capacity of the gas at constant volume in $J/K$ is:

Which of the following substances has the maximum specific heat capacity?

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