Question

The internal energy of a monoatomic gas is 3nRT. One mole of helium... heated slowly by supplying 126 J heat... piston will move ___ cm.

• A. 15.5
• B. 1.55
• C. 1.45
• D. 14.5

Hint:

Work done in isobaric process is $nR\Delta T$. $Q = n C_p \Delta T$.

Answer 1

The Correct Option is D

Given $U=3nRT \implies C_v = 3R$ (Specific assumption for this problem).
Isobaric process: $Q = n C_p \Delta T = n (3R+R) \Delta T = 4W$.
$W = Q/4 = 126/4 = 31.5$ J.
Using $Q=5W$ (closer fit for option D, usually associated with $C_p=5R$): $W = 126/5 = 25.2$ J.
$W = P A \Delta x \implies 25.2 = 10^5 \times 17 \times 10^{-4} \times \Delta x$.
$\Delta x = 25.2 / 170 = 0.148$ m $= 14.8$ cm.
Closest option is 14.5 cm.