A metal ball of mass 0.1 kg is heated upto 50 0 ∘ C 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 3 0 ∘ C . What is

Question

A metal ball of mass 0.1 kg is heated upto 50 0 ∘ C 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 3 0 ∘ C . What 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 ]

TestHub · Accepted Answer

Assume final temperature = T ∘ C Heat lass = Heat gain = ms Δ T ⇒ m B ​ s B ​ Δ T B ​ = m w ​ s w ​ Δ T w ​ 0.1 × 400 × ( 500 − T ) = 0.5 × 4200 × ( T − 30 ) + 800 ( T − 30 ) ⇒ 40 ( 500 − T ) = ( T − 30 ) ( 2100 + 800 ) ⇒ 20000 − 40 T = 2900 T − 30 × 2900 ⇒ 20000 + 30 × 2900 = T ( 2940 ) T = 30. 4 ∘ C T Δ T ​ × 100 = 30 6.4 ​ × 100 = 21% so the closest answer is 20% .

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