One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system

Question

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 ${cm}^{2}$ . The gas is heated slowly to raise the temperature by $1.2 ° C$ during which the piston moves by 25 mm. The amount of heat supplied to the gas is ______ J. (Atmospheric pressure = 100 kPa, R = 8.3 J/mol·K) (Neglect mass of the piston) [2026]

Smart Achievers · Accepted Answer

(2)

$Q = Δ U + W$

$Q = \frac{f}{2} n R Δ T + P Δ V$

$Diatomic gas f = 5$

$Q = \frac{5}{2} \times 1 \times 8.3 \times 1.2 + 100 \times 10^{3} (4 \times 10^{- 4} \times 0.025)$

$Q = 24.9 + 1 = 25.9 J, nearest answer is 25$

$Here, please note that instead of the above method, if we use Q = n C_{p} Δ T, then also no option matches.$

Solution

1 24.8

2 25

3 15.04

4 29.98

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