When two non reactive samples at different temperatures are mixed in an isolated container of negligible heat capacity the final temperature of the mixture can be:

Options

A. lesser than lower or greater than higher temperature is
B. equal to lower or higher temperature
C. greater than lower but lesser than higher temperature
D. average of lower and higher temperatures

Explanation

To solve the problem of determining the possible final temperatures when two non-reactive samples at different temperatures are mixed in an isolated container of negligible heat capacity, we can follow these steps:

### Step 1: Understand the Problem
We have two samples with different temperatures, T1 and T2, where T2 > T1. The container has negligible heat capacity, meaning it does not absorb any heat itself.

### Step 2: Apply the Principle of Calorimetry
When the two samples are mixed:
- The hotter sample (T2) will lose heat.
- The colder sample (T1) will gain heat.

### Step 3: Determine the Final Temperature Range
Since the hotter sample loses heat and the colder sample gains heat, the final temperature (T) of the mixture will be:
- Greater than the temperature of the colder sample (T1).
- Less than the temperature of the hotter sample (T2).

Thus, we can express this mathematically as:
\[ T1 < T < T2 \]

### Step 4: Analyze the Options
Now, we analyze the given options based on our understanding:

1. **Option A: Less than the lower temperature** - This is incorrect because T is greater than T1.
2. **Option B: Equal to lower or higher temperature** - This is correct because if the hotter sample cools down to T1, the final temperature can be equal to T1.
3. **Option C: Greater than lower and less than higher temperature** - This is correct as we established that T1 < T < T2.
4. **Option D: Average of lower and higher temperature** - This can also be correct because the final temperature can be the average value of T1 and T2, satisfying the condition T1 < T < T2.

### Conclusion
The correct options are B, C, and D.

### Summary of Final Temperature Conditions:
- The final temperature can be equal to the lower temperature (T1).
- The final temperature is always greater than the lower temperature (T1) and less than the higher temperature (T2).
- The final temperature can also be the average of T1 and T2.