Consider two containers A and B containing monoatomic gases at the same Pressure P , Volume V and Temperature T . The gas in A is compressed isothermally to 1 8 of its original volume while the gas in B is compressed adiabatically to 1 8 of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Step-by-step solution

In an isothermal process the temperature is constant. P V = n R T So, it can be written that P V = P A V 8 ⇒ P A = 8 P In an adiabatic process, P V γ = constant γ for monoatomic gas is 5 3 So, it can be written P B P = V V 8 5 3 ⇒ P B = 32 P Thus, the ratio of the pressures is P B P A = 32 P 8 P = 4