An ideal gas is enclosed in a cyclinder with a movable piston on top. The piston has mass of 8000g and an area of `5.00cm^2` and is free to slide up and down, keeping the pressure of the gas constant. How much work is done as the temperature of `0.200mol` of the gas is raised from `200^@C` to `300^@C`?

Explanation

To solve the problem, we need to calculate the work done when the temperature of an ideal gas is raised while keeping the pressure constant. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Mass of the piston, \( m = 8000 \, \text{g} = 8 \, \text{kg} \)
- Area of the piston, \( A = 5.00 \, \text{cm}^2 = 5.00 \times 10^{-4} \, \text{m}^2 \)
- Number of moles of gas, \( n = 0.200 \, \text{mol} \)
- Initial temperature, \( T_1 = 200^\circ C = 200 + 273.15 = 473.15 \, \text{K} \)
- Final temperature, \( T_2 = 300^\circ C = 300 + 273.15 = 573.15 \, \text{K} \)

### Step 2: Calculate the change in temperature
\[ \Delta T = T_2 - T_1 = 573.15 \, \text{K} - 473.15 \, \text{K} = 100 \, \text{K} \]

### Step 3: Use the ideal gas constant
The ideal gas constant \( R \) is given as:
\[ R = 8.31 \, \text{J/(mol K)} \]

### Step 4: Calculate the work done
The work done at constant pressure can be calculated using the formula:
\[ W = nR\Delta T \]
Substituting the known values:
\[ W = (0.200 \, \text{mol}) \times (8.31 \, \text{J/(mol K)}) \times (100 \, \text{K}) \]
\[ W = 0.200 \times 8.31 \times 100 = 166.2 \, \text{J} \]

### Final Answer
The work done as the temperature of the gas is raised from \( 200^\circ C \) to \( 300^\circ C \) is \( 166.2 \, \text{J} \).

---