Question

Find the change in internal energy of a gas if its temperature changes by \(10\,\text{K}\). Number of moles of gas is \(10\), \(C_p\) (specific heat at constant pressure) is \(7\,\text{cal\,K}^{-1}\text{mol}^{-1}\) and \(R\) (gas constant) \(= 2\,\text{cal\,K}^{-1}\text{mol}^{-1}\).

• A. \(500\,\text{cal}\)
• B. \(1000\,\text{cal}\)
• C. \(250\,\text{cal}\)
• D. \(100\,\text{cal}\)

Hint:

For ideal gases:
Internal energy depends only on temperature
Always use \(C_v\) for calculating \(\Delta U\)
Relation: \(C_p - C_v = R\)

Answer 1

The Correct Option is A

Step 1: Use the relation between molar heat capacities: \[ C_p - C_v = R \] \[ C_v = C_p - R = 7 - 2 = 5\,\text{cal\,K}^{-1}\text{mol}^{-1} \]
Step 2: Change in internal energy of an ideal gas is: \[ \Delta U = n C_v \Delta T \]
Step 3: Substitute the given values: \[ \Delta U = 10 \times 5 \times 10 = 500\,\text{cal} \]