A certain gas is isothermally compressed to ( 1 3 )^ rd of its initial volume ( V_o = 3 litre) by applying required pressure. If the bulk modulus of the gas is 3 10^5 N/m ^2 , the magnitude of work done on the gas is _______ J.

Step-by-step solution

For an isothermal process, the isothermal bulk modulus equals the gas pressure: B_T = -V dP dV Since PV = constant , differentiating gives P ,dV + V ,dP = 0 , so dP dV = - P V , which yields B_T = P . Therefore, the initial pressure is: P_o = 3 10^5 N/m ^2 Volumes: V_o = 3 L = 3 10⁻³ m ^3 V_f = 1 3 V_o = 10⁻³ m ^3 Work done on the gas during an isothermal compression: W_ on = -W_ by = -P_o V_o ( V_f V_o ) = P_o V_o ( V_o V_f ) W_ on = (3 10^5)(3 10⁻³) 3 W_ on = 900 3 J Using 3 1.0986 : W_ on 900 1.0986 988.74 J Rou