A gas is compressed from a volume of 2m3 to a volume of 1 `m^3` at a constant pressure of 100 N/`m^2`. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas:

Options

A. increases by 250 J
B. decreases by 250 J
C. increases by 50 J
D. decreases by 50 J

Explanation

To find the change in internal energy of the gas, we can follow these steps:

### Step 1: Identify the Given Information
- Initial volume (V_initial) = 2 m³
- Final volume (V_final) = 1 m³
- Constant pressure (P) = 100 N/m²
- Heat supplied (Q) = 150 J

### Step 2: Calculate the Change in Volume (ΔV)
The change in volume (ΔV) can be calculated as:
\[ \Delta V = V_{\text{final}} - V_{\text{initial}} = 1 \, \text{m}^3 - 2 \, \text{m}^3 = -1 \, \text{m}^3 \]

### Step 3: Calculate the Work Done (W) on the Gas
Since the gas is compressed at constant pressure, the work done on the gas can be calculated using the formula:
\[ W = P \cdot \Delta V \]
Substituting the values we have:
\[ W = 100 \, \text{N/m}^2 \cdot (-1 \, \text{m}^3) = -100 \, \text{J} \]
(Note: The work done on the gas is negative because the gas is compressed.)

### Step 4: Use the First Law of Thermodynamics
According to the first law of thermodynamics:
\[ Q = \Delta U + W \]
Rearranging this gives us:
\[ \Delta U = Q - W \]
Substituting the values of Q and W:
\[ \Delta U = 150 \, \text{J} - (-100 \, \text{J}) = 150 \, \text{J} + 100 \, \text{J} = 250 \, \text{J} \]

### Step 5: Conclusion
The change in internal energy (ΔU) of the gas is:
\[ \Delta U = 250 \, \text{J} \]