A small quantity mass m, of water at a temperature `theta ("in " ^(@)C)` is poured on to a larger mass M of ice which is at its melting point. If c is the specific heat capacity of water and L the specific heat capacity of water and L the specific latent heat of fusion of ice, then the mass of ice melted is give by

Options

A. `4.2 xx 10^3`
B. `3.0 xx 10^3`
C. `1.2 xx 10^3`
D. `1.5 xx 10^3`

Answer

D

Explanation

On the X scale , the temperature difference between the boiling and freezing points is
` 305 x- 25 x = 280 X `
on the `""^@ C` scale , it is `100^@ - 0^@ = 100^@ C `
thus , a temperature difference of 280 X is equal to a temperature difference of `100^@ C`
` therefore ` for a ` 1 ^@C ` change in `""^@ C` scale there is a corresponding 2.8 X change in X scale
Specific heat capacity of water `= 4200 J kg^(-1) ""^@ C^(-1)`
Specific heat capacity of water in this new scale is
`=(4200 )/( 2.8 ) j Kg^(-1) X^(-1) = 1500 j Kg^(-1) x^(-1) = 1. 5 xx 10^3 J kg ^(-1) X^(-1)`