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The specific heat capacities of some metals (in J g−1 K−1) are given below. Copper: 0.385 Magnesium: 1.020 Mercury: 0.138 Platinum: 0.130 If 100 kJ of heat is added to 10.0 g samples of each of the metals above, all at 25°C, determine which metal will have the smallest increase in temperature.

Sagot :

Answer: Magnesium metal will have the smallest increase in temperature.

Explanation:

Given: Specific heats are as follows.

Copper = 0.385 J/g K,     Magnesium = 1.020 J/g K

Mercury = 0.138 J/g K,     Platinum = 0.130 J/g K

Heat energy = 100 kJ  (1 kJ = 1000 J) = 100000 J

mass = 10.0 g

Initial temperature = [tex]25^{o}C[/tex]

Formula used to calculate the increase in temperature for each of the given elements is as follows.

[tex]q = m \times C \times (T_{2} - T_{1})[/tex]

where,

q = heat energy

m = mass

C = specific heat

[tex]T_{1}[/tex] = initial temperature

[tex]T_{2}[/tex] = final temperature

  • The change in temperature for copper is calculated as follows.

[tex]q = m \times C \times (T_{2} - T_{1})\\100000 = 10.0 g \times 0.385 J/g K \times (T_{2} - 25)\\T_{2} = 25999.026^{o}C[/tex]

  • The change in temperature for magnesium is calculated as follows.

[tex]q = m \times C \times (T_{2} - T_{1})\\100000 = 10.0 g \times 1.020 J/g K \times (T_{2} - 25)^{o}C\\T_{2} = 9828.92^{o}C[/tex]

  • The change in temperature for mercury is calculated as follows.

[tex]q = m \times C \times (T_{2} - T_{1})\\100000 = 10.0 g \times 0.138 J/g K \times (T_{2} - 25)^{o}C\\T_{2} = 72488.77^{o}C[/tex]

  • The change in temperature for platinum is calculated as follows.

[tex]q = m \times C \times (T_{2} - T_{1})\\100000 = 10.0 g \times 0.130 J/g K \times (T_{2} - 25)^{o}C\\T_{2} = 76948.08^{o}C[/tex]

Thus, we can conclude that magnesium metal will have the smallest increase in temperature.

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