A new metal alloy is found to have a specific heat capacity of 0.321 J / (g⋅∘C). First, 44.5 g of the new alloy is heated to 100. ∘C. Then, it is placed in an ideal constant-pressure calorimeter containing 175 g of water (Vs, water=4.184 J / (g⋅∘C)) at an initial temperature of 20.0 ∘C. What will the final temperature of the mixture be after it attains thermal equilibrium

Question

Physics

Ivan Olsen

11 April, 11:56

A new metal alloy is found to have a specific heat capacity of 0.321 J / (g⋅∘C). First, 44.5 g of the new alloy is heated to 100. ∘C. Then, it is placed in an ideal constant-pressure calorimeter containing 175 g of water (Vs, water=4.184 J / (g⋅∘C)) at an initial temperature of 20.0 ∘C. What will the final temperature of the mixture be after it attains thermal equilibrium

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Answers (1)

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Levi Mcgee · Answer 1

The final temperature is 21.531°c

Explanation:

Heat gained by the water = heat lost by the metal

Heat gained = (m) (c) (∆tita)

Where m = mass

C = specific heat capacity

∆tita = temperature change

X = equilibrium temperature

So ...

Heat gained by water

= 175*4.185 * (x-20)

= 732.2x - 14644

Heat lost by metal

= 44.5*0.321 * (100-x)

=1428.45 - 14.2845x

So ...

1428.45 - 14.2845x = 732.2x - 14644

1428.45+14644 = 732.2x + 14.2845x

16072.45 = 746.4845x

16072.45/746.4845 = x

21.531 = x

The final temperature is 21.531°c