Question

W much heat transfer is necessary to raise the temperature of a 0.200-kg piece of ice from −20.0°C to 130.0°C, including the energy needed for phase changes?

How much time is required for each stage, assuming a constant 20.0 kJ/s rate of heat transfer?
Make a graph of temperature versus time for this process.

Answer 1

The heat transfer required to raise the temperature of a 0.200-kg piece of ice from −20.0°C to 130.0°C, including phase changes, can be calculated using the formula
`\( Q = mc\Delta T \)` for temperature changes and ( Q = mL ) for phase changes.

Step-by-step explanation:

First, we calculate the heat transfer for temperature changes using the formula
`\( Q = mc\Delta T \)`, where m is the mass, c is the specific heat capacity, and
`\( \Delta T \)` is the change in temperature. For the phase changes, we use ( Q = mL ), where L is the latent heat of fusion or vaporization. Summing up these values gives the total heat transfer.

For time calculation, we use the formula
`\( \text{time} = \frac{\text{total heat transfer}}{\text{rate of heat transfer}} \)`. Given the constant rate of 20.0 kJ/s, we convert this to joules and divide the total heat transfer by this rate to find the time.

The graph of temperature versus time for this process would have distinct segments corresponding to temperature changes and phase transitions. Temperature increases linearly during heating phases, and plateaus represent phase changes where the temperature remains constant. The resulting graph illustrates the dynamic nature of the heating process, with different slopes and plateaus indicating varying rates of temperature change and energy absorption during phase transitions.