If the mass of each molecule of a gas is halved and speed is doubled , find the ratio of initial and final pressure.

Explanation

Let initial and final pressures be `P_1 and P_2`
Here, `M_1 = M, C_1 = C, V_1 = V,`
`M_2 = M//@, C_2=2C,V_2=V,`
As `P_1 = 1/3 M_1/V_1C_1^2`
`P_2 =1/3M_2/V_2C_2^2`
Ratio of pressure :
`:.P_1/P_2=M_1/M_2xxV_2/V_1xxC_1^2/C_2^2`
`=M/(M//2)xxV/Vxx(C/(2C))^2=1/2`