(C) The kinetic energy of the bullet when it returns to the point of departure is $K = \frac{1}{2}mv^2$. Given $m = 50 \ g = 0.05 \ kg$ and $v = 840 \

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(C) The kinetic energy of the bullet when it returns to the point of departure is $K = \frac{1}{2}mv^2$. Given $m = 50 \ g = 0.05 \ kg$ and $v = 840 \ m/s$. $K = \frac{1}{2} \times 0.05 \times (840)^2 = 17640 \ J$. Converting this to calories $(1 \ cal = 4.2 \ J)$: $Q_1 = \frac{17640}{4.2} = 4200 \ cal$. Additionally,the bullet cools from $30^{\circ}C$ to $0^{\circ}C$,releasing heat $Q_2 = mc\Delta T$. $Q_2 = 50 \times 0.02 \times (30 - 0) = 30 \ cal$. Total heat available $Q = Q_1 + Q_2 = 4200 + 30 = 4230 \ cal$. Using $Q = mL_f$,where $L_f = 80 \ cal/g$: $m_{ice} = \frac{4230}{80} = 52.875 \ g$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Mix Examples-Thermometry, Thermal Expansion and Calorimetry

Difficult

$A$ lead bullet of mass $50 \ g$ at a temperature of $30^{\circ}C$ is fired vertically upwards with a speed of $840 \ m/s$. When the bullet returns to the point of departure,it strikes a large block of ice at $0^{\circ}C$. How much ice (in $g$) will melt? (Specific heat of lead is $0.02 \ cal/g^{\circ}C$,latent heat of fusion of ice is $80 \ cal/g$,and assume all energy is used to melt the ice.)

A
$62.7$
B
$55$
C
$52.875$
D
$50.67$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Mix Examples-Thermometry, Thermal Expansion and Calorimetry

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The thermo $e.m.f.$ of a thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700\,^{\circ}C$. If the cold junction is kept at $0\,^{\circ}C$,then the neutral temperature is:

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$A$ thermocouple develops $40\,\mu V/K$. If the hot and cold junctions are at $40\,^{\circ}C$ and $20\,^{\circ}C$ respectively,then the emf developed by a thermopile using $150$ such thermocouples in series shall be ............... $mV$.

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Work done in converting one gram of ice at $-10^{\circ}C$ into steam at $100^{\circ}C$ is ....... $J$

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