When unit mass of water boils to become steam at `100^(@)C`, it absorbs Q amount of heat. The densities of water and steam at `100^(@)C` are `rho_(1)` and `rho_(2)` respectively and the atmospheric pressure is `P_(0)`. The increase in internal energy of the water is

Options

A. `Q`
B. `Q +P_(0)((1)/(rho_(1)) - (1)/(rho_(2)))`
C. `Q + P_(0)((1)/(rho_(2)) - (1)/(rho_(1)))`
D. `Q - P_(0)((1)/(rho_(1)) + (1)/(rho_(2)))`

Answer

B

Explanation

`Q = DeltaU +W implies +Q = DeltaU +P_(0)(V_(2)-V_(1))`
` implies Q = DeltaU + P_(0)((1)/(rho_(2))- (1)/(rho_(1))) implies DeltaU = Q + P_(0)((1)/(rho_(1))-(1)/(rho_(2)))`