JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
- JEE Mains 2019
- Hard
- Numerical
A metal bal of mass \(0.1\, kg\) is heated upto \(500\,{}^oC\) and dropped into a vessel of heat capacity \(800\, JK^{-1}\) and containing \(0.5\, kg\) water. The initial temperature of water and vessel is \(30\,{}^oC\). ........ \(\%\) is the approximate percentage increment in the temperature of the water. [Specific heat Capacities of water and metal are, respectively \(4200\, Jkg^{-1}K^{-1}\) and \(400\, Jkg^{-1}K^{-1}\)]
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(20\)
Step-by-step Solution
Detailed explanation
\(0.1 \times 400 \times \left( {500 - T} \right)\)
\( = 0.5 \times 4200 \times \left( {T - 30} \right) + 800\left( {T - 30} \right)\)
\( \Rightarrow 40\left( {500 - T} \right) = \left( {T - 30} \right)\left( {2100 + 800} \right)\)
\( \Rightarrow 20000 - 40T = 2900\,T - 30 \times 2900\)
\( \Rightarrow 20000 + 30 \times 2900 = T\left( {2940} \right)\)
\(T = {30.4^ \circ }C\)
\(\frac{{\Delta T}}{T} \times 100 = \frac{{6.4}}{{30}} \times 100 \simeq 20\% \)
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