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50 g of an alloy containing 60% copper a...

50 g of an alloy containing `60%` copper and `40%` nickel is dropped in 55 g of water at `10^(@)C`, kept in a calorimeter of water equivalent 5 g. The final temperature becomes `20^(@)C`. What was the initial temperature of the alloy? Specific heats of copper and nickel are `"0.095 cal.g"^(-1).^(@)C^(-1)` and `"0.11 cal.g"^(-1).^(@)C^(-1)` respectively.

Text Solution

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Let the masses of copper and nickel in the alloy be `m_(1)` and `m_(2)` respectively and the initial temperature of the alloy be t. From the fundamental principle of calorimetry,
heat lost by the alloy = heat gained by water and the calorimeter
`"i.e., "(m_(1)s_(1)+m_(2)s_(2))(t-20)=(55+5)xx1xx(20-10)`
`"or, "t=(600)/(m_(1)s_(1)+m_(2)s_(2))+20`
Given, `m_(1)=50xx(60)/(100)=30g, m_(2)=50xx(40)/(100)=20g`.
`s_(1)=0.095 and s_(2)=0.11`
`therefore" "t=(600)/(30xx0.095+20xx0.11)+20=138.81^(@)C`
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