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A block of aluminum with a mass of 2.0 kg has an initial temperature of 20°C. It absorbs 7300 J of thermal energy. The specific heat capacity of aluminum is 913 J/(kg°C).

What is the final temperature of the aluminum block?

A) 4.0°C
B) 8.0°C
C) 24°C
D) 28°C

Answer :

To solve this problem, we need to use the formula for calculating the change in temperature when a specific amount of thermal energy is absorbed by a material. The formula is:

[tex]\Delta T = \frac{Q}{m \cdot c}[/tex]

Where:

  • [tex]\Delta T[/tex] is the change in temperature (in degrees Celsius),
  • [tex]Q[/tex] is the heat absorbed (in joules),
  • [tex]m[/tex] is the mass of the substance (in kilograms),
  • [tex]c[/tex] is the specific heat capacity of the substance (in [tex]J/(kg \cdot °C)[/tex]).

Given values:

  • [tex]Q = 7300[/tex] J
  • [tex]m = 2.0[/tex] kg
  • [tex]c = 913[/tex] J/(kg°C)

First, calculate the change in temperature:

[tex]\Delta T = \frac{7300}{2.0 \cdot 913}[/tex]

[tex]\Delta T = \frac{7300}{1826}[/tex]

[tex]\Delta T \approx 4.0 \text{°C}[/tex]

The initial temperature of the aluminium block is 20°C. To find the final temperature, we add the change in temperature to the initial temperature:

Final Temperature = Initial Temperature + Change in Temperature

Final Temperature = 20°C + 4.0°C = 24°C

Thus, the final temperature of the aluminium block is 24°C.

The correct multiple-choice option is C) 24°C.

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