Express the relations between the pressure and the temperature and between the volume and the temperature in an adiabatic process. 

Answer

`(p//p_0)^(gamma-1)=(T//T_0)^(gamma-1)=T_0//T`

Explanation

From the Poission equation, we obtain `p_(ad) = p_(0)(V_0//V)^(gamma) = 4 xx 10^(5) xx 4^(1.4) = 4^(2.4) xx 10^(5)`. For the case of isothermic compression we obtain `p_(isot) = 4p_0`, i.e., a pressure almost twice as small.
The work of adiabatic compression of a gas is
`W_(ad) = (p_2V_2 - p_1V_1)//(gamma - 1) = 1.87 xx 10^(6) J`
The work of isothermic compression of a gas is
`W_(isot) = 2.3 p_1V_1 "log" (V_1//V_2) = 1.11 xx 10^6 J`.