Figure shows the variation of internal energy `(U)` with the pressure `(P)` of `2.0` mole gas in cyclic process abcda.The temperature of gas at c and d are `300 and 500 K` respectively. The heat absorbed by the gas during the process is `Xxx 10 R ln 2` . Find the value of x.

Options

A. 40
B. 20
C. 100
D. 300

Answer

A

Explanation

Change in internal energy for cyclic process `Delta U = 0`
For process ` a to b,` (P is constant ), `W_(a to b) = P * Delta V = nR Delta T = - 400 R `
For process `b to C` (T is constant ), `W _(b to c) = -2 R(300)" In "2`
For process `d to a` (T is constant ), `W_(d to a) = +2R (500 )"in 2"`
Net work
`(Delta W) = W_(a to b) + W_(b to c) + W_(o to d) + W _(d to a) ," " Delta W =" 400 R In 2"`
dQ=dU+ dW , first law os thermodynamics `"dQ = 400 R In 2"`