Question

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A piece of unknown metal with mass 68.6 g is heated to an initial temperature of 100 °C and dropped into 8.4 g of water (with an initial temperature of 20 °C) in a calorimeter. The final temperature of the system is 52.1°C. The specific heat of water is 4.184 J/g*⁰C. What is the specific heat of the metal?

A. 0.171
B. 0.343
C. 1.717
D. 3.433

Answer 1

B

Step-by-step explanation:

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Answer 2

Answer:- B. 0.343

Solution:- Hot metal is added to water so the heat is gained by water and lost by the metal. We assume no heat is lost to the surroundings, so the heat lost by metal is totally used to raise the temperature of water.

First, we will calculate the heat gained by water using the formula:

`q=mc\Delta T`

where, q is the heat energy, m is the mass, c is specific heat and delta T is change in temperature.

For water:

m = 8.4 g

c =
`(4.184J)/(g.^0C)`

`\Delta T=52.1-20=32.1 ^0C`

Let's plug in the values and calculate q for water:

`q=(8.4g)((4.184J)/(g.^0C))(32.1^0C)`

= 1128.17 J

Same amount of heat is lost by the metal. Mass of metal is 68.6 g.

`\Delta T=100-52.1=47.9^0C`

let's plug in the values in the same formula and calculate the specific heat of metal:

`1128.17J=(68.6g)(c)(47.9^0C)`

`c=(1128.17J)/((68.6g)(47.9^0C))`

`c=(0.343J)/(g.^0C)`

So, the right choice is B.0.343.