Calculate the specific heat of copper if it takes 23 cal (96 J) to heat a 5.0 g sample from 25 degree C to 75 degree C.

Verified step by step guidance

1. Identify the formula for specific heat: \( q = mc\Delta T \), where \( q \) is the heat absorbed or released, \( m \) is the mass, \( c \) is the specific heat, and \( \Delta T \) is the change in temperature.
2. Rearrange the formula to solve for specific heat \( c \): \( c = \frac{q}{m\Delta T} \).
3. Calculate the change in temperature \( \Delta T \): \( \Delta T = T_{\text{final}} - T_{\text{initial}} = 75^\circ C - 25^\circ C \).
4. Substitute the given values into the rearranged formula: \( q = 23 \text{ cal} \), \( m = 5.0 \text{ g} \), and \( \Delta T \) from the previous step.
5. Calculate the specific heat \( c \) using the substituted values.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a material-specific property that indicates how well a substance can store thermal energy. For example, copper has a specific heat capacity that reflects its ability to absorb heat, which is crucial for calculations involving temperature changes.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this context, the heat absorbed by the copper sample is calculated using the formula Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Understanding this concept is essential for solving the problem.

Units of Measurement

Units of measurement are standard quantities used to express physical properties. In this question, heat is measured in calories and joules, while mass is measured in grams. It is important to be aware of these units and their conversions, as they play a critical role in accurately calculating specific heat and ensuring consistency in scientific calculations.