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I heat 29.292 g of an unknown metal up to 99.9 °C. While it is heating, I weigh out 27.777 g of water and find its initial temperature is 22.1 °C. When I mix the metal and water in an insulated container, the temperature of the mixture rises to 29.3 °C.

What is the most likely specific heat of the metal?

Select one:

a. 4.8 (10^4) cal/(g°C)
b. 9.7 (10^2) cal/(g°C)
c. 7.9 (10^3) cal/(g°C)
d. 0.13 cal/(g°C)
e. 9.8 (10^5) cal/(g°C)

Answer :

The specific heat capacity of the metal, given that 27.777 g of water at 22.1 °C was mixed with the metal is 9.7×10⁻² Cal/gºC

How do I determine the specific heat capacity of the metal?

Step 1: Obtain the heat absorbed by the water. This is shown below:

  • Mass of water (M) = 27.777 g
  • Initial temperature (T₁) = 22.1 °C
  • Final temperature (T₂) = 29.3 °C
  • Temperature change (ΔT) = 29.3 - 22.1 = 7.2 °C
  • Specific heat capacity of water (C) = 1 Cal/gºC
  • Heat absorbed (Q) =?

Q = MCΔT

= 27.777 × 1 × 7.2

= 199.9944 Cal

Step 2: Determine the specific heat capacity of the metal using the heat absorbed by the water. Details below:

  • Heat absorbed by water (Q) = 199.9944 Cal
  • Heat released by metal (Q) = -199.9944 Cal
  • Mass of metal (M) = 29.292 g
  • Initial temperature (T₁) = 99.9 °C
  • Final temperature (T₂) = 29.3 °C
  • Temperature change (ΔT) = 29.3 - 99.9 = -70.6 °C
  • Specific heat capacity of metal (C) = ?

Q = MCΔT

-199.9944 = 29.292 × C × -70.6

-199.9944 = -2068.0152 × C

Divide both sides by -2068.0152

C = -199.9944 / -2068.0152

= 9.7×10⁻² Cal/gºC

Thus, the specific heat capacity of the metal is 9.7×10⁻² Cal/gºC. None of the options are correct.

Learn more about specific heat capacity:

https://brainly.com/question/19104255

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