Answer :
To solve the problem of determining the total change in temperature of the sample, we can follow these steps:
1. Understand the initial and final conditions:
- The sample starts at room temperature, which is 300 K.
- It is then heated to an oven temperature of 500 K.
- After that, it cools back down to room temperature, which is again 300 K.
2. Calculate the temperature change during the heating process:
- The sample is initially at 300 K and is heated to 500 K.
- The change in temperature during the heating phase is:
[tex]\[
\Delta T_{\text{heating}} = 500\,\text{K} - 300\,\text{K} = 200\,\text{K}
\][/tex]
3. Calculate the temperature change during the cooling process:
- The sample cools from 500 K back down to 300 K.
- The change in temperature during the cooling phase is:
[tex]\[
\Delta T_{\text{cooling}} = 300\,\text{K} - 500\,\text{K} = -200\,\text{K}
\][/tex]
- Note that the cooling results in a negative change because the temperature decreases.
4. Determine the total change in temperature (absolute change):
- To find the total change in temperature, consider the absolute change during both processes:
[tex]\[
\text{Total change} = \Delta T_{\text{heating}} + |\Delta T_{\text{cooling}}|
\][/tex]
- Substitute the values we calculated:
[tex]\[
\text{Total change} = 200\,\text{K} + 200\,\text{K} = 400\,\text{K}
\][/tex]
Therefore, the total change in temperature ([tex]\( \Delta T \)[/tex]) for the entire process of heating and cooling is 400 K.
1. Understand the initial and final conditions:
- The sample starts at room temperature, which is 300 K.
- It is then heated to an oven temperature of 500 K.
- After that, it cools back down to room temperature, which is again 300 K.
2. Calculate the temperature change during the heating process:
- The sample is initially at 300 K and is heated to 500 K.
- The change in temperature during the heating phase is:
[tex]\[
\Delta T_{\text{heating}} = 500\,\text{K} - 300\,\text{K} = 200\,\text{K}
\][/tex]
3. Calculate the temperature change during the cooling process:
- The sample cools from 500 K back down to 300 K.
- The change in temperature during the cooling phase is:
[tex]\[
\Delta T_{\text{cooling}} = 300\,\text{K} - 500\,\text{K} = -200\,\text{K}
\][/tex]
- Note that the cooling results in a negative change because the temperature decreases.
4. Determine the total change in temperature (absolute change):
- To find the total change in temperature, consider the absolute change during both processes:
[tex]\[
\text{Total change} = \Delta T_{\text{heating}} + |\Delta T_{\text{cooling}}|
\][/tex]
- Substitute the values we calculated:
[tex]\[
\text{Total change} = 200\,\text{K} + 200\,\text{K} = 400\,\text{K}
\][/tex]
Therefore, the total change in temperature ([tex]\( \Delta T \)[/tex]) for the entire process of heating and cooling is 400 K.
