Question

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

• A. 500 cal
• B. 1000 cal
• C. 250 cal
• D. 100 cal

Hint:

When solving for changes in internal energy, remember that for an ideal gas, \( \Delta U = n C_V \Delta T \), and use the relationship between \( C_P \) and \( C_V \) to find the required value.

Answer 1

The Correct Option is A

Step 1: Use the relationship between heat and internal energy change.
The change in internal energy \( \Delta U \) is given by: \[ \Delta U = nC_V \Delta T \] Where \( C_V \) is the specific heat at constant volume, and it is related to \( C_P \) by the equation \( C_P - C_V = R \). Thus, \[ C_V = C_P - R = 7 - 2 = 5 \, \text{cal/K-mol} \] Step 2: Calculate the change in internal energy.
Given that \( n = 10 \) moles, \( C_V = 5 \, \text{cal/K-mol} \), and \( \Delta T = 10 \, \text{K} \), we can calculate \( \Delta U \): \[ \Delta U = 10 \times 5 \times 10 = 500 \, \text{cal} \] Step 3: Conclusion.
The change in internal energy is 500 cal, which corresponds to option (1).