Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium `M_(1) = 4g` and that of hydrogen `M_(2) = 2g`
If the internal energy of He sample is `100J` and that of the hydrogen sample is `200J` , then the internal energy of the mixture is

Options

A. `900J`
B. `128.5J`
C. `171.4J`
D. `300J`

Explanation

To find the internal energy of the mixture of helium and hydrogen, we can follow these steps:

### Step 1: Understand the given data
- Moles of helium (He) = 5 moles
- Molar mass of helium (M1) = 4 g/mol
- Internal energy of helium sample (U_He) = 100 J
- Moles of hydrogen (H2) = 2 moles
- Molar mass of hydrogen (M2) = 2 g/mol
- Internal energy of hydrogen sample (U_H2) = 200 J

### Step 2: Calculate the total internal energy of the mixture
The internal energy of a mixture of ideal gases can be calculated by simply adding the internal energies of the individual gases, as they do not interact in a way that changes their internal energy during mixing.

\[ U_{mixture} = U_{He} + U_{H2} \]

### Step 3: Substitute the values into the equation
Now we can substitute the values of internal energy for helium and hydrogen into the equation:

\[ U_{mixture} = 100 J + 200 J \]

### Step 4: Perform the addition
Now, we perform the addition:

\[ U_{mixture} = 300 J \]

### Conclusion
The internal energy of the mixture is 300 J.

### Final Answer
The internal energy of the mixture is **300 J**.

---