The pressure at `C` is

Answer

`1869.75`

Explanation

Work done by the gas in the process `W_(AB) =( (nRT_A -T_B))/(gamma -1) = (R(T_A - T_B))/(5/3 -1)`
or `W_(AB) = 3/2 R(T_A - T_B)" ...(i)"`
Now for an adiabatic process
`rArr" "P_(A)^(gamma-1) T)A^(- gamma) = P_B^(gamma -1) T_b^(-gamma)`
or `(P_A/P_B)^(r-1) = (T_A/T_B)^(gamma)" ....(ii)"`
or `(3/2)^(5//3-1) =(T_A/T_B )^(5//3)" "["Given "P_B = 2/3 P_A]`
`(3/2)^(2//3) = (T_A/T_B)^(5//3)" or "T_B = (2/3)^(2//5)xx1000 = 850 K`
`W_(AB) = 3/2 xx8.31 xx(1000-850) = 1869.75 J`