Question

A piece of silver with a mass of \(362 \mathrm{~g}\) has a heat capacity of \(85.7 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). What is the specific heat of silver?

Short answer

The specific heat of silver is \(0.237 \mathrm{~J}/(\mathrm{g} \cdot ^{\circ}\mathrm{C})\).

Step-by-step solution

Identify the Given Values

The mass of silver is given as \(362 \mathrm{~g}\), and the heat capacity is given as \(85.7 \mathrm{~J}/^{\circ}\mathrm{C}\).

Recall the Formula

The formula for specific heat \(c\) is \(c = \frac{C}{m}\), where \(C\) is the heat capacity and \(m\) is the mass of the substance.

Substitute the Values into the Formula

Substitute the given values into the formula: \(c = \frac{85.7 \mathrm{~J}/^{\circ}\mathrm{C}}{362 \mathrm{~g}}\).

Calculate the Specific Heat

Perform the division to find the specific heat of silver: \(c = 0.237 \mathrm{~J}/(\mathrm{g} \cdot ^{\circ}\mathrm{C})\).

Key concepts

Calculation of Specific Heat

To determine the specific heat of a substance, we can use a simple formula. Specific heat is a measure of how much heat energy is required to raise the temperature of 1 gram of a substance by 1 degree Celsius. It is expressed in units of energy per unit temperature per unit mass, commonly joules per gram per degree Celsius (J/g°C). The formula for specific heat (\( c \) ) is:\[c = \frac{C}{m} \]where \( C \) represents the heat capacity of the substance, and \( m \) is its mass.Consider the exercise involving a piece of silver. We are given the heat capacity as 85.7 J/°C and the mass as 362 g. By directly substituting these values into our formula, we find the specific heat of silver to be 0.237 J/(g°C).

• This process involves identifying what is given: mass and heat capacity.
• Recalling the specific heat formula and substituting the values.
• Performing the calculation by dividing the heat capacity by the mass.

Once you understand this, you can apply it to find the specific heat of various substances by changing their mass and heat capacity in the formula.

Heat Capacity

Heat capacity is an important physical property that indicates how much heat a substance can store per degree temperature change. It provides insight into the thermal stability and heat absorption ability of a material. Unlike specific heat, which is a property of the material itself and is normalized by mass, heat capacity (\( C \) ) is dependent on the object's overall size and mass. It is expressed in joules per degree Celsius (J/°C).For instance, in the silver exercise, the given heat capacity is 85.7 J/°C.Heat capacity helps in comparing how different masses of the same substance or different substances react to gain or lose heat. It's helpful:

• When looking at larger bodies of material where specific heat might not be intuitive.
• When calculating the total energy change in thermal processes.
• For understanding the overall energy storage capability of the substance.

Understanding heat capacity aids in discerning how a substance will interact thermally and is crucial in industrial and scientific applications involving temperature control.

Mass and Specific Heat Relation

The relationship between mass and specific heat is quite straightforward yet essential in understanding thermal properties.Specific heat (\( c \) ) is the amount of heat per unit mass required to change the temperature of a substance by one degree Celsius. This means it normalizes the heat capacity according to mass, offering a 'per gram' or 'per kilogram' perspective.The formula shows this relationship:\[c = \frac{C}{m} \]If you increase the mass of a substance while keeping the material and its conditions constant, the total heat capacity (\( C \) ) increases, but specific heat (\( c \) ) remains the same.

• Specific heat allows for fair comparisons between different substances, regardless of their mass.
• It's integral in calculations that require comparing thermal energy absorption on a per-mass basis.
• Knowing this relation helps in designing experiments and industrial applications where precise thermal management is crucial.

In thermal problems, always remember the interplay between mass and specific heat to accurately determine how much energy is necessary for temperature changes in materials.