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 of finding the new pressure of a gas when it is heated in a sealed container, we can follow these steps:

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

### Step 2: Use the Ideal Gas Law Relationship
Since the volume of the container is constant, we can use the relationship derived from the ideal gas law, which states that:
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]
Where:
- \( P_1 \) = initial pressure
- \( P_2 \) = final pressure
- \( T_1 \) = initial temperature
- \( T_2 \) = final temperature

### Step 3: Rearrange the Equation to Solve for P2
We can rearrange the equation to solve for the final pressure \( P_2 \):
\[ P_2 = P_1 \times \frac{T_2}{T_1} \]

### Step 4: Substitute the Known Values
Now, substitute the known values into the equation:
\[ P_2 = 2.00 \, \text{atm} \times \frac{40.0 \, \text{K}}{20.0 \, \text{K}} \]

### Step 5: Calculate P2
Now perform the calculation:
\[ P_2 = 2.00 \, \text{atm} \times 2 = 4.00 \, \text{atm} \]

### Final Answer
The new pressure \( P_2 \) is 4.00 atm.

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