Question

Calculate the heat capacity of a piece of wood if 1500.0 g of the wood absorbs 6.75×10⁴ joules of heat, and its temperature changes from 32°C to 57°C

Answer 1

The heat capacity of the piece of wood is approximately 450 J/°C.

Explanation:

When determining the heat capacity, the formula Q = mcΔT is a fundamental equation in thermodynamics. In this context, we applied it to find the specific heat capacity (c) of the wood. By rearranging the formula, we isolated the specific heat capacity and substituted the given values for mass (m), temperature change (ΔT), and heat absorbed (Q). The resulting calculation yielded a specific heat capacity of approximately 450 J/°C for the piece of wood.

This value signifies the amount of heat energy required to raise the temperature of the wood by 1 degree Celsius. Understanding specific heat capacities is crucial in various scientific and engineering applications, providing insights into how different materials respond to thermal energy transfer.

Answer 2

The heat capacity C of the piece of wood is
`\( 1800 \text{ J/(kg} \cdot \text{°C)} \).`

To calculate the heat capacity of a piece of wood, follow these steps:

1. Determine the mass of the wood:

Given:
`\(1500.0 \text{ g}\)`. To use the formula for heat capacity, we need to convert this mass into kilograms because the specific heat capacity is typically expressed in
`\( \text{J/(kg} \cdot \text{°C)} \).`

`\[ 1500.0 \text{ g} = 1.500 \text{ kg} \]`

2. Calculate the change in temperature (
`\( \Delta T \))`:

Change in temperature:
`\( \Delta T = T_{\text{final}} - T_{\text{initial}} \) \[ \Delta T = 57°C - 32°C = 25°C \]`

3. Calculate the heat absorbed ( Q ):

Given:
`\( Q = 6.75 * 10^4 \text{ joules} \)`

4. Apply the formula for heat capacity( C ):

The formula to calculate the specific heat capacity ( c ) is:

`\[ c = (Q)/(m \cdot \Delta T) \]`

where Q is the heat absorbed, m is the mass in kilograms, and
`\( \Delta T \)` is the change in temperature.

5. Solve for the specific heat capacity:

Plug in the known values and solve for c :

`\[ c = \frac{6.75 * 10^4 \text{ J}}{1.500 \text{ kg} \cdot 25°C} \]`

When we perform the calculation, we find that the specific heat capacity of the wood is
`\( 1800 \text{ J/(kg} \cdot \text{°C)} \).`