Five moles of hydrogen gas are heated from `30^(@)C` to `60^(@)C` at constant pressure. Heat given to the gas is (given `R = 2 cal//mol` degrees)

Options

A. 750 cal
B. 630 cal
C. 1050 cal
D. 1470 cal

Answer

To find the heat given to the gas when 5 moles of hydrogen gas are heated from \(30^\circ C\) to \(60^\circ C\) at constant pressure, we can use the formula for heat transfer at constant pressure:

\[ \Delta Q = n C_P \Delta T \]

Where:
- \(\Delta Q\) is the heat added to the gas,
- \(n\) is the number of moles of the gas,
- \(C_P\) is the specific heat capacity at constant pressure,
- \(\Delta T\) is the change in temperature.

### Step 1: Identify the values
- Number of moles, \(n = 5\) moles
- Change in temperature, \(\Delta T = 60^\circ C - 30^\circ C = 30^\circ C\)
- Universal gas constant, \(R = 2 \, \text{cal/mol} \cdot \text{K}\)

### Step 2: Calculate \(C_P\) for diatomic hydrogen gas
For a diatomic gas like hydrogen (\(H_2\)), the specific heat capacity at constant pressure is given by:

\[ C_P = \frac{7}{2} R = 3.5 R \]

Substituting the value of \(R\):

\[ C_P = 3.5 \times 2 \, \text{cal/mol} \cdot \text{K} = 7 \, \text{cal/mol} \cdot \text{K} \]

### Step 3: Calculate \(\Delta Q\)
Now we can substitute the values into the heat transfer equation:

\[ \Delta Q = n C_P \Delta T \]
\[ \Delta Q = 5 \, \text{moles} \times 7 \, \text{cal/mol} \cdot \text{K} \times 30 \, \text{K} \]

Calculating this gives:

\[ \Delta Q = 5 \times 7 \times 30 = 1050 \, \text{calories} \]

### Final Answer
The heat given to the gas is \(1050 \, \text{calories}\).

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