In chemistry the volume for a certain gas is given by V=20T, where V is measured in cc and T is temperature in °C. If the temperature varies between 80°C and 130°C

 , find the set of volume values.

 

Enter the exact answer in interval notation.

 

To enter ∞
, type infinity. To enter ∪, type U.

To determine the range of volume values for the gas as the temperature \( T \) varies from 80°C to 130°C, we start by substituting the temperature bounds into the volume equation \( V = 20T \).

1. **Find the volume at the lower temperature bound, \( T = 80 \):**
   \[
   V = 20 \times 80 = 1600 \text{ cc}
   \]

2. **Find the volume at the upper temperature bound, \( T = 130 \):**
   \[
   V = 20 \times 130 = 2600 \text{ cc}
   \]

Since the equation \( V = 20T \) is a linear function with a positive coefficient, \( V \) increases as \( T \) increases. Therefore, as \( T \) ranges from 80 to 130, \( V \) will range from 1600 to 2600.

3. **Express the volume range in interval notation:**
   \[
   V \in [1600, 2600]
   \]

So, the exact answer in interval notation is:
\[
[1600, 2600]
\]

Would you like further details on this solution or have any questions?

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### Related Questions:
1. How would the volume range change if the temperature varied from 50°C to 100°C?
2. What is the physical meaning of a linear relationship between volume and temperature for gases?
3. How would you solve if the relationship was \( V = 30T + 10 \) instead?
4. What would be the volume if the temperature is decreased to 0°C?
5. How does this formula relate to Charles's Law in thermodynamics?

### Tip:
For linear equations like \( V = kT \), the range of \( V \) over a temperature interval \([T_1, T_2]\) is simply the set of values between \( kT_1 \) and \( kT_2 \).

In chemistry the volume for a certain gas is given by V=20T, where V is measured in cc and T is temperature in °C. If the temperature varies between 80°C and 130°C, find the set of volume values. Enter the exact answer in interval notation. To enter ∞, type infinity. To enter ∪, type U.

Explore how to calculate the volume range of a gas with V=20T when temperature varies between 80°C and 130°C. This problem involves algebraic concepts and interval notation, ideal for high school students studying linear functions and gas behavior.

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