Question

An ideal mono-atomic gas is heated at constant pressure. The fraction of the total energy applied which increases the internal energy for the gas is

• A. \(\frac{3}{5}\)
• B. \(\frac{5}{3}\)
• C. \(\frac{7}{5}\)
• D. \(\frac{5}{7}\)

Hint:

At constant pressure the heat is \(nC_p\Delta T\) and the internal energy change is \(nC_v\Delta T\).

Answer 1

The Correct Option is A

Step 1: Use molar specific heats
For a monatomic gas $C_v=\dfrac{3}{2}R$ and $C_p=\dfrac{5}{2}R$.

Step 2: Ratio
$\dfrac{C_v}{C_p}=\dfrac{3}{5}$.

Step 3: Compare the options
$\dfrac{5}{3}$ is $\gamma$, and $\dfrac{7}{5}$ and $\dfrac{5}{7}$ belong to a diatomic gas; a fraction cannot exceed 1.

Final Answer:
The fraction of heat that increases internal energy is 3/5. \[ \boxed{\text{(A) }\dfrac{3}{5}} \]