The change in internal energy when 5 mole of hydrogen is heated to `20^(@)C` from `10^(@)C`, specific heat of hydrogen at constant pressure is 8 cal/mol`.^(@)C` is

Options

A. 200 cal
B. 350 cal
C. 300 cal
D. 475 cal

Answer

To solve the problem of finding the change in internal energy when 5 moles of hydrogen are heated from 10°C to 20°C, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Number of moles (n) = 5 moles
- Initial temperature (Ti) = 10°C
- Final temperature (Tf) = 20°C
- Specific heat at constant pressure (Cp) = 8 cal/mol·°C

2. **Calculate the Change in Temperature (ΔT):**
\[ \Delta T = T_f - T_i = 20°C - 10°C = 10°C \]

3. **Use Mayer's Relation to Find Cv:**
Mayer's relation states:
\[ C_p - C_v = R \]
where R is the gas constant. For hydrogen, R = 2 cal/mol·°C.
\[ C_v = C_p - R = 8 \text{ cal/mol·°C} - 2 \text{ cal/mol·°C} = 6 \text{ cal/mol·°C} \]

4. **Calculate the Change in Internal Energy (ΔU):**
The formula for change in internal energy is:
\[ \Delta U = n \cdot C_v \cdot \Delta T \]
Substituting the values:
\[ \Delta U = 5 \text{ moles} \cdot 6 \text{ cal/mol·°C} \cdot 10°C \]
\[ \Delta U = 5 \cdot 6 \cdot 10 = 300 \text{ cal} \]

### Final Answer:
The change in internal energy (ΔU) is **300 calories**.

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