Question

Find change in internal energy of gas if its temperature changes by $10$ K. 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) is $2$ cal/K.

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

Hint:

Internal energy of an ideal gas depends only on temperature, not on pressure or volume. Always use $C_v$ (not $C_p$) when calculating change in internal energy.

Answer 1

The Correct Option is A

Concept: For an ideal gas, the change in internal energy depends only on the change in temperature and is given by: \[ \Delta U = n C_v \Delta T \] The specific heats at constant pressure and volume are related by: \[ C_p = C_v + R \]
Step 1: Find $C_v$ Given: \[ C_p = 7 \text{ cal/K-mol}, \quad R = 2 \text{ cal/K} \] \[ C_v = C_p - R = 7 - 2 = 5 \text{ cal/K-mol} \]
Step 2: Write the formula for change in internal energy \[ \Delta U = n C_v \Delta T \]
Step 3: Substitute values \[ \Delta U = (10)(5)(10) \] \[ \Delta U = 500 \text{ cal} \] Conclusion: The change in internal energy of the gas is: \[ \boxed{500 \text{ cal}} \]