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A woman working in the field drinks her ...

A woman working in the field drinks her morning coffee out of an aluminium cup. The cup has a mass of 0.120 kg and is initially at `20.0^(@)C` when she pours in 0.300 kg of coffee initially at `70.0^(@)C`. What is te final temperature after the coffee and the cup attain thermal equilibrium? (Assume that coffee has the same specific heat as water and that there is no heat exchange with the surroundings).

Text Solution

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`Q_("coffee")=m_("coffee")DeltaT_("coffee")`
`Q_("coffee")=(0.300kg)(4190J//kg.K)(T-70.0^(@)C)`
The positive heat is gained by the aluminium cup is ltBrgt `Q_("aluminium")=M_("aluminium").C_("aluminium")DeltaT_("aluminium")` ltBrgt `=(0.120kg)(910J//kg.K)(T-20.0^(@)C)`
We equate the sum of these two quantities of heat to zero, obtaining an algebraic equation for T.
`Q_("coffee")=Q_("aluminium")=0`
`(0.300kg)(4190J//kg.K)(T-70.0^(@)C)+(0.120kg)(910J//kg.K)(T-20.0^(@)C)=0`
`T=66.0^(@)C`.
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