The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross sectional area of 17 $c m ²$ and fitted with a light movable frictionless piston. The gas is heated slowly by supplying 126 J heat. If the temperature rises by 4 $° C,$ then the piston will move ____ cm.
(atmospheric pressure = $10^{5}$ Pa) [2026]

Question

Smart Achievers · Accepted Answer

(1)

$Δ U = 3 n R Δ T$

$Δ U = 3 \times 1 \times \frac{25}{3} \times 4 = 100 Joule$

$Δ Q = 126$

$W = 26 = P Δ V$

$26 = 10^{5} \times 17 \times 10^{- 4} Δ x$

$Δ x = \frac{26}{170} = 15.3$

Solution

1 15.5

2 1.45

3 14.5

4 1.55

Ans.
(1)

$Δ U = 3 n R Δ T$

$Δ U = 3 \times 1 \times \frac{25}{3} \times 4 = 100 Joule$

$Δ Q = 126$

$W = 26 = P Δ V$

$26 = 10^{5} \times 17 \times 10^{- 4} Δ x$

$Δ x = \frac{26}{170} = 15.3$

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