Water at `0^@C` contained in a closed vessel, is abruptly opened in an evacuated chamber. If the specific latent heats of fusion and vapourization at `0^@C` are in the ratio `lamda:1` the fraction of water eveporated will be

Options

A. `lamda//1`
B. `lamda//(lamda+1)`
C. `(1-lamda)//lamda`
D. `(lamda-1)//(lamda+1)`

Answer

B

Explanation

Given `("latent heat of fusion")/("latent heat of vapourization")=(lamda)/(1)=(L_f)/(L_v)(say)`
i.e., `L_f=lamdaL-v`
Now, if k is required fraction.
Then, `(1-k)L_f=kL_v`
or `((1-k))/(k)=(1)/(lamda)` or `(1)/(k)=(1)/(lamda)+1`
or `k=(lamda)/(lamda+1)`