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: Understanding the Concept
At constant pressure, heat supplied is \(Q=nC_p\Delta T\), while the rise in internal energy is \(\Delta U=nC_v\Delta T\).

Step 2: Fraction
\(\dfrac{\Delta U}{Q}=\dfrac{C_v}{C_p}=\dfrac{1}{\gamma}\).

Step 3: Calculation
For a monatomic gas \(\gamma=\dfrac{5}{3}\), so the fraction is \(\dfrac{3}{5}\). The remaining \(\dfrac{2}{5}\) is spent as work of expansion.

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