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Water at `506(@)C` is filled in a closed cylindercal vessel of height `10cm` and cross sectional area `10cm^(2)` The walls of the vessel are adiabatic but the flat parts are made of `1-mm` thick aluminium `(K=200Js^(-2)m^(-1)`^(@)C^(-1)` . Assume that the outside temperature is `20^(@)C` . The density of water is `1000kgm^(-3)` and the specify heat capacity of water `=4200Jkg^(-1)`^(@)C^(-1)` .Estimate the time taken for the temperature to fall by `1.0^(@)C` . Make any simplifying assumotion you need but speify them. |
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Answer» Correct Answer - C `A=10 cm^(2): H=10 cm` `( Delta Q)/( Delta T)=(kA(T_1-T_2))/(l)` `=(200xx10xx10^(-4)xx30)/(1xx10^(-3))` `6000 J//s` Since heat goes out form both surfaces hence net heat coming out `( Delta Q)/( Delta T)=6000xx2=12000` `( Delta Q)/( Delta T)=ms ( Delta T)/( Delta l) `implies6000xx2=10^(-3)xx10^(-1)xx1000` `xx4200xx( Delta Q)/( Delta T).` `implies( Delta Q)/( Delta T)=12000/420=28.57` so in one sec 28.57^(@)C is dropped Hence time to drop of `1^(@)C=(1)/(28.57)sec.` `=0.035 sec is required . |
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