28g of `N_(2)`gas at 300 K and 20 atm was allowed to expand isothermally against a constant external pressure of 1 atm , q for the gas is `(R=0.082)`.

Options

A. 2495 J
B. 7473 J
C. 2367 J
D. 2570 J

Answer

C

Explanation

Intial volume `(V_1) " for " N_2 (PV_1 = nRT)`
`20 xx V_1 =((28)/(28))xx 0.082 xx 300 therefore V_1 = 1.23 ` litres
Final volume `(V_2) " for N_2 (P V_2= nRT) `
`1 xx V_2 = (28/28) xx 0.082 xx 300 rArr therefore V_2 = 24.60 `litre
Since expansion is made against constant pressure and thus irreversible.
`P= atm = 1.013 xx 10^5 Nm^(-2)`
`Delta V= (V_2 -V_1)= (24.60 -1.23) Lit = 23.37 xx 10^(-3)`
`= -23. 67 xx 10^(2) J `
`therefore q = Delta U - W =0 + 23.67 xx 10^2 = + 23.67 xx 10^2 = + 2367 J`
`( because Delta =0` in an internal expansion )