An irregular lump of an unknown metal has a measured density of 5.50 g/mL. The metal is heated to a temperature of 153 °C and placed in a graduated cylinder filled with 25.0 mL of water at 25.0 °C. After the system has reached thermal equilibrium, the volume in the cylinder is read at 30.0 mL, and the temperature is recorded as 41.0 °C. What is the specific heat of the unknown metal sample? Assume no heat is lost to the surroundings.

Answer :

Answer: [tex]0.543J/g^0C[/tex]

Explanation:

Volume of metal = volume of water displaced = (30.0 - 25.0) ml = 5.0 ml

Density of metal = 5.50 g/ml

Mass of metal =[tex]density\times volume =5.50\times 5.0=27.5g[/tex]

Volume of water = 25.0 ml

Density of metal = 1.0 g/ml

Mass of metal =[tex]density\times volume =1.0\times 25.0=25.0g[/tex]

[tex]heat_{absorbed}=heat_{released}[/tex]

As we know that,  

[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]

[tex]-[m_1\times c_1\times (T_{final}-T_1)]=[m_2\times c_2\times (T_{final}-T_2)][/tex]         .................(1)

where,

q = heat absorbed or released

[tex]m_1[/tex] = mass of metal = 27.5 g

[tex]m_2[/tex] = mass of water = 25.0 g

[tex]T_{final}[/tex] = final temperature = ?[tex]41.0^0C[/tex]

[tex]T_1[/tex] = temperature of metal = [tex]153^oC[/tex]

[tex]T_2[/tex] = temperature of water = [tex]25.0^oC[/tex]

[tex]c_1[/tex] = specific heat of lead = ?

[tex]c_2[/tex] = specific heat of water= [tex]4.184J/g^0C[/tex]

Now put all the given values in equation (1), we get

[tex]27.5g\times c_1\times (41.0-153)^0C=[25.0g\times 4.814J/g^0C\times (41.0-25.0)^0C][/tex]

[tex]c_1=0.543J/g^0C[/tex]

Thus the specific heat of the unknown metal sample is [tex]0.543J/g^0C[/tex]

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