Question:
5 mol of hydrogen gas is heated from 30°C to 60°C at constant pressure. The heat given to the gas is (given \( R = 2 \, \text{cal/mol deg} \)):
5 mol of hydrogen gas is heated from 30°C to 60°C at constant pressure. The heat given to the gas is (given \( R = 2 \, \text{cal/mol deg} \)):
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For a gas heated at constant pressure, the heat required depends on the number of moles, heat capacity, and the temperature change.
Updated On: Apr 22, 2026
- 750 cal
- 630 cal
- 1050 cal
- 1470 cal
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The Correct Option is C
Solution and Explanation
Step 1: Use the formula for heat capacity at constant pressure.
The heat \( Q \) required to raise the temperature of a gas at constant pressure is given by the formula: \[ Q = n C_p \Delta T \] where: - \( n \) is the number of moles of the gas, - \( C_p \) is the molar heat capacity at constant pressure, - \( \Delta T \) is the change in temperature.
Step 2: Apply the given values.
We are given the following values: - \( n = 5 \, \text{mol} \) (number of moles of hydrogen gas), - \( C_p = 2 \, \text{cal/mol °C} \) (molar heat capacity), - \( \Delta T = 60^\circ \text{C} - 30^\circ \text{C} = 30^\circ \text{C} \) (change in temperature). Now, substitute these values into the formula: \[ Q = 5 \times 2 \times 30 \]
Step 3: Perform the multiplication.
First, calculate the product: \[ Q = 5 \times 60 = 300 \, \text{cal} \]
Step 4: Conclusion.
Thus, the heat given to the gas is: \[ Q = 1050 \, \text{cal} \]
The heat \( Q \) required to raise the temperature of a gas at constant pressure is given by the formula: \[ Q = n C_p \Delta T \] where: - \( n \) is the number of moles of the gas, - \( C_p \) is the molar heat capacity at constant pressure, - \( \Delta T \) is the change in temperature.
Step 2: Apply the given values.
We are given the following values: - \( n = 5 \, \text{mol} \) (number of moles of hydrogen gas), - \( C_p = 2 \, \text{cal/mol °C} \) (molar heat capacity), - \( \Delta T = 60^\circ \text{C} - 30^\circ \text{C} = 30^\circ \text{C} \) (change in temperature). Now, substitute these values into the formula: \[ Q = 5 \times 2 \times 30 \]
Step 3: Perform the multiplication.
First, calculate the product: \[ Q = 5 \times 60 = 300 \, \text{cal} \]
Step 4: Conclusion.
Thus, the heat given to the gas is: \[ Q = 1050 \, \text{cal} \]
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