# what is the change in thermal energy of the block of aluminum A) 187 J B) 2,590 J C) 5820 J D)187,000 JThe temperature of a 24.5-g block of aluminum decreases from 30. degree C to 21.5 degree C if...

what is the change in thermal energy of the block of aluminum

A) 187 J

B) 2,590 J

C) 5820 J

D)187,000 J

The temperature of a 24.5-g block of aluminum decreases from 30. degree C to 21.5 degree C if aluminum has specific heat of 897 J/kg degree C

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Heat energy, Q, is found by the product of the mass of an object times the temperature change times the specific heat of the material.

Q = m * c * delta T

You are given the specific heat of 897 J/kg-degree C

In this case the change in temperature is 8.5 degrees C (30 - 21.5)

But you only have 24.5 g of aluminium, or 0. 0245 kg.

= 8.5 * 897 * 0.0245 = 187 J

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Looking for the change in thermal energy means finding the heat change in the sample.   For that we use the following equation

q = m * s * deltaT

where q is the heat, m is the mass, s is the specific heat, and deltaT is the change in temperature (final - initial).  So that the units will cancel, we need to convert the mass from g to kg by dividing by 1000.

q = (0.0245 kg)(897 J/kg degC)(21.5-30 deg C)

q = (0.0345 kg)(897 J/kg degC)(-8.5 deg C)

The negative sign indicates that the Al is losing energy as it cools but the change is a positive value.

Multiply through the values to find the value of q.