What is the change internal energy when a gas contracts from 377 mL to 177 mL under a constant pressure of 1520 torr, while at the same time being cooled by removing 124 J heat ?
`[Take :( 1 L atm ) =100 J)]`

Options

A. 40.52 J
B. `-83.48 J`
C. `-248 J`
D. None of these

Explanation

To find the change in internal energy (ΔU) of the gas when it contracts from 377 mL to 177 mL under a constant pressure of 1520 torr while removing 124 J of heat, we can follow these steps:

### Step 1: Calculate the Work Done (W)
The work done by the gas during contraction can be calculated using the formula:
\[ W = -P \Delta V \]
Where:
- \( P \) is the pressure in atm,
- \( \Delta V \) is the change in volume in liters.

First, we need to convert the pressure from torr to atm:
\[ P = \frac{1520 \text{ torr}}{760 \text{ torr/atm}} = 2 \text{ atm} \]

Next, we calculate the change in volume (ΔV):
\[ \Delta V = V_2 - V_1 = 177 \text{ mL} - 377 \text{ mL} = -200 \text{ mL} \]
Convert mL to liters:
\[ \Delta V = -200 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = -0.2 \text{ L} \]

Now, substitute the values into the work formula:
\[ W = -P \Delta V = -2 \text{ atm} \times (-0.2 \text{ L}) = 0.4 \text{ L atm} \]

Convert work from L atm to Joules using the conversion \( 1 \text{ L atm} = 100 \text{ J} \):
\[ W = 0.4 \text{ L atm} \times 100 \text{ J/L atm} = 40 \text{ J} \]

### Step 2: Calculate the Heat Transfer (Q)
The heat transfer (Q) is given as:
\[ Q = -124 \text{ J} \]
(The negative sign indicates that heat is being removed from the system.)

### Step 3: Apply the First Law of Thermodynamics
According to the first law of thermodynamics:
\[ \Delta U = Q + W \]

Substituting the values we calculated:
\[ \Delta U = -124 \text{ J} + 40 \text{ J} = -84 \text{ J} \]

### Final Answer
The change in internal energy (ΔU) is:
\[ \Delta U = -84 \text{ J} \]

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