Question

The specific heat of nickel is \[0.44J/g^\circ C\]. How much energy needed to change the temperature of \[95.4g\] of nickel from \[32^\circ C\] to \[22^\circ C\]. Is the energy absorbed or released?

Answer 1

Hint: Specific heat is the amount of heat which is required to raise the temperature of a substance with unit mass by one degree. The energy absorbed or released is denoted by a positive or negative sign.

Complete step by step answer:
When a substance undergoes a change of temperature from one state to another state, heat is either absorbed or released. When a substance goes from lower to higher temperature energy is absorbed during the process. When a substance goes from higher to lower temperature energy is released during the process.
So at first we have to note the initial and the final temperature of the substance. The substance in this case is nickel metal. The initial temperature is \[32^\circ C\]. It undergoes temperature change to a final temperature \[22^\circ C\].
The final temperature is lower than the initial temperature. Thus from the concept heat is released in this process.
The magnitude of the heat absorbed or released is calculated using the change in temperature. The relation is given as
$Q = m{c_p}\Delta T$where \[Q\] is the heat absorbed or released, \[m\] is the mass of the substance, \[{c_p}\]is the specific heat of that substance, and \[T\] is the temperature change.
The specific heat is the ratio of heat capacity of the substance and the mass of the substance. It is denoted by \[{c_p}\]. It is also defined as the amount of heat required to increase the temperature by one degree of a substance with unit mass.
Given \[m = 95.4g\], \[{c_p} = 0.44J/g^\circ C\] , \[\Delta T = 22 - 32 = - 10^\circ C\]
Inserting the values in the equation, the heat released is
$Q = 95.4g \times 0.44J{g^{ - 1}}^\circ {C^{ - 1}} \times ( - 10^\circ C) = - 419.76J$

The energy needed to change the temperature of \[95.4g\] of nickel from \[32^\circ C\] to \[22^\circ C\] is $419.76J$.

Note: From the calculation the heat is found to contain a negative sign which confirms that heat is released. The specific heat capacity is a function of pressure and temperature. The subscript p stands for constant pressure. When the volume is kept constant the specific heat is denoted as \[{c_v}\].