Question

10 mole of oxygen is heated at constant volume from 30 \(^{\circ}\)C to 40 \(^{\circ}\)C. The change in the internal energy of the gas is_____ cal.
(The molecular specific heat of oxygen at constant pressure, \(C_p=7\) cal/mol \(^{\circ}\)C and \(R=2\) cal/mol \(^{\circ}\)C.)

Hint:

\(\Delta U = nC_v \Delta T\) is valid for ideal gases in ANY process, not just isochoric. For isochoric process, \(Q = \Delta U\).

Answer 1

Correct Answer: 500

Step 1: Formula for Internal Energy:
Change in internal energy depends on \(C_v\) and \(\Delta T\): \[ \Delta U = n C_v \Delta T \] Step 2: Find \(C_v\):
Using \(C_p - C_v = R\): \[ 7 - C_v = 2 \implies C_v = 5 \, \text{cal/mol}^{\circ}\text{C} \] Step 3: Calculate \(\Delta U\):
\(n = 10\) mol. \(\Delta T = 40 - 30 = 10 \, ^{\circ}\text{C}\) (or K). \[ \Delta U = 10 \times 5 \times 10 = 500 \, \text{cal} \] Step 4: Final Answer:
500