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JIPMER 2005
Exam
JIPMER
Year
2005
Subject
Physics
Chapter
Thermal Properties of Matter

JIPMER 2005 · Physics · Thermal Properties of Matter

A body of specific heat 0.2 kcal / kg^ C is heated through 100^ C ....

A body of specific heat 0.2kcal/kg∘C0.2 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C} is heated through 100∘C100^{\circ} \mathrm{C}. The percentage increase in its mass is

Options

  1. A9%9 \%
  2. B9.3×10−11%9.3 \times 10^{-11} \%
  3. C10%10 \%
  4. DNone of these

Correct answer

B. 9.3×10−11%9.3 \times 10^{-11} \%

Step-by-step solution

Heat taken by the given body =mcΔθ=m c \Delta \theta {specific heat of body =0.2kcal/kg∘C=0.2 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}, final temperature of the body \left.=100^{\circ} \mathrm{C}\right\} ΔE=m×0.2×100=20mkcal=20 m×4.2×103 J\begin{aligned} \Delta E & =m \times 0.2 \times 100=20 \mathrm{mkcal} \\ & =20 \mathrm{~m} \times 4.2 \times 10^3 \mathrm{~J}\end{aligned}NowgaininmassisgivenbyNow gain in mass is given by\Delta m=\frac{\Delta E}{C^2} \left(\because E=m c^2\right)=20 m×4.2×103(3×108)2=\frac{20 \mathrm{~m} \times 4.2 \times 10^3}{\left(3 \times 10^8\right)^2} Therefore, percentage increase in mass is given by =Δmm×100=20m×4.2×103(3×108)2×m×100=9.3×10−11%\begin{aligned} & =\frac{\Delta m}{m} \times 100 \\ & =\frac{20 m \times 4.2 \times 10^3}{\left(3 \times 10^8\right)^2 \times m} \times 100 \\ & =9.3 \times 10^{-11} \%\end{aligned}
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