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A 425-g piece of metal at 100°C is dropped into a 100-g aluminum cup containing 500 g of water at 15°C. The final temperature of the system is 40°C. What is the specific heat of the metal, assuming no heat is exchanged with the surroundings? The specific heat of aluminum is 900 J/kg°C.

a. 2140 J/(kg•K)
b. 3800 J/(kg•K)
c. 3300 J/(kg•K)
d. 1900 J/(kg•K)
e. 4280 J/(kg•K)

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The specific heat of the metal, assuming no heat is exchanged with the surroundings is 2140 J/(kg•K).

Specific heat capacity of the metal

The specific heat capacity of the metal is determined from the principle of conservation of energy.

energy lost by the metal = energy gained by aluminum + energy gained by water

Q = mcΔθ

where;

  • m is mass (kg)
  • c is specific heat capacity
  • Δθ is change in temperature

0.425c(100 - 40) = 0.1(900)(40 - 15) + 0.5(4186)(40 - 15)

25.5c = 2250 + 52,325

c = 54,575/25.5

c = 2140 J/(kg•K)

Learn more about specific heat capacity here: https://brainly.com/question/21406849

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