Two containers A and B contain monoatomic gases at the same pressure P, volume V and temperature T. Gas A is compressed isothermally to V/8, while gas B is compressed adiabatically to V/8. The ratio of final pressure of gas B to final pressure of gas A is:
Options

Question

Two containers A and B contain monoatomic gases at the same pressure P, volume V and temperature T. Gas A is compressed isothermally to V/8, while gas B is compressed adiabatically to V/8. The ratio of final pressure of gas B to final pressure of gas A is:

Options

G1 Physics · Accepted Answer

For gas A, isothermal compression gives PV = P(A)(V/8) Therefore, P(A) = 8P For monoatomic gas, γ = 5/3 For gas B, adiabatic compression gives PV^γ = P(B)(V/8)^γ Therefore, P(B) = P·8^(5/3) Hence, P(B)/P(A) = 8^(5/3)/8 = 8^(2/3) = 4 Hence option B follows.