Question

The oxygen gas of 5 moles is heated at constant pressure from 300 K to 320 K. The amount of energy spent during this expansion is 
(For oxygen \( C_p = 7 \, {Cal/mol} \cdot \degree C \), \( C_v = 5 \, {Cal/mol} \cdot \degree C \)) 
 

• A. 200 Cal
• B. 250 Cal
• C. 350 Cal
• D. 100 Cal

Hint:

For constant pressure processes, the energy spent is calculated using \( Q = n C_p \Delta T \), where \( C_p \) is the specific heat at constant pressure.

Answer 1

The Correct Option is A

The problem asks for the energy spent during the expansion, which is the work done. 
We know that \( C_p - C_v = R \), where \( R \) is the ideal gas constant. Given \( C_p = 7 \, {Cal/mol} \cdot \degree C \) and \( C_v = 5 \, {Cal/mol} \cdot \degree C \), we can find \( R \): \[ R = C_p - C_v = 7 - 5 = 2 \, {Cal/mol} \cdot \degree C \] The work done at constant pressure is given by: \[ W = nR\Delta T \] 
We are given \( n = 5 \) moles and \( \Delta T = 320 \, {K} - 300 \, {K} = 20 \, {K} \). 
Substituting the values, we get: \[ W = 5 \, {moles} \times 2 \, {Cal/mol} \cdot \degree C \times 20 \, \degree C = 200 \, {Cal} \] Therefore, the amount of energy spent during the expansion is 200 Cal.