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)

Step-by-step solution

Using the first law of thermodynamics: Q = U + W Since the gas is diatomic with rotational modes only, the degrees of freedom are f = 5 , so: C_V = 5 2 R For n = 1 mole and T = 1.2 K : U = nC_V T = 1 5 2 8.3 1.2 = 24.9 J Work done by the gas: W = P , V Cross-sectional area of the piston: A = 4 cm ^2 = 4 10⁻⁴ m ^2 Piston displacement: x = 25 mm = 2.5 10⁻² m Change in volume: V = A x = (4 10⁻⁴)(2.5 10⁻²) = 1 10⁻⁵ m ^3 With P = 100 kPa = 10^5 Pa : W = (10^5)(1 10⁻⁵) = 1 J Therefore, the heat supplied is: Q = U + W = 2