A gas occupies 2 litre at STP. It is provided 58.63 joule heat so that its volume becomes 2.5litre at 1 atm. Calculate change in its internal energy

Options

A. 8.63
B. 7.62
C. 12.9
D. 5.54

Answer

To calculate the change in internal energy (\( \Delta U \)) of the gas, we can follow these steps:

### Step 1: Identify the initial and final conditions
- Initial volume (\( V_1 \)) = 2 liters
- Final volume (\( V_2 \)) = 2.5 liters
- Pressure (\( P \)) = 1 atm
- Heat provided (\( Q \)) = 58.63 joules

### Step 2: Calculate the work done (\( W \))
The work done on/by the gas during expansion can be calculated using the formula:
\[ W = -P \Delta V \]
Where \( \Delta V = V_2 - V_1 \).

Calculating \( \Delta V \):
\[ \Delta V = 2.5 \, \text{liters} - 2.0 \, \text{liters} = 0.5 \, \text{liters} \]

Now substituting the values into the work done formula:
\[ W = -P \Delta V = -1 \, \text{atm} \times 0.5 \, \text{liters} \]

### Step 3: Convert work done to joules
1 liter-atmosphere is equal to 101.325 joules. Therefore:
\[ W = -0.5 \, \text{liters} \times 101.325 \, \text{joules/liter-atm} = -50.66 \, \text{joules} \]

### Step 4: Use the first law of thermodynamics to find \( \Delta U \)
According to the first law of thermodynamics:
\[ \Delta U = Q + W \]
Substituting the values of \( Q \) and \( W \):
\[ \Delta U = 58.63 \, \text{joules} + (-50.66 \, \text{joules}) = 58.63 - 50.66 = 7.97 \, \text{joules} \]

### Final Answer
The change in internal energy (\( \Delta U \)) is approximately:
\[ \Delta U \approx 7.97 \, \text{joules} \]