A sealed container with gas at 2.00 atm is heated from 20.0 K to 40.0 K. The new pressure is:

Options

A. 0.050 atm
B. 1.00 atm
C. 4.00 atm
D. 2.14 atm

Explanation

To solve the problem, we will use the relationship between pressure and temperature for a gas in a sealed container, which is derived from the ideal gas law. Here are the steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial pressure (P1) = 2.00 atm
- Initial temperature (T1) = 20.0 K
- Final temperature (T2) = 40.0 K

2. **Use the Direct Proportionality of Pressure and Temperature**:
- According to the ideal gas law, for a sealed container, the pressure of the gas is directly proportional to its absolute temperature. This can be expressed as:
\[ \frac{P1}{P2} = \frac{T1}{T2} \]
- Rearranging this gives us:
\[ P2 = P1 \times \frac{T2}{T1} \]

3. **Substitute the Known Values**:
- Plugging in the values we have:
\[ P2 = 2.00 \, \text{atm} \times \frac{40.0 \, \text{K}}{20.0 \, \text{K}} \]

4. **Calculate the New Pressure**:
- Performing the calculation:
\[ P2 = 2.00 \, \text{atm} \times 2 = 4.00 \, \text{atm} \]

5. **Conclusion**:
- The new pressure (P2) after heating the gas is 4.00 atm.

### Final Answer:
The new pressure is **4.00 atm**.

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