J $2.$ A bucket is filled with ice chips at a temperature of $-40C.$ A glass containing $0\mathrm{.}50$ kg of water at a temperature of $0C$ is poured onto the ice chips. When the system reaches thermal equilibrium it is all ice and the temperature is $-35C.$ Given that the specific heat of ice is $2\mathrm{.}0k\frac{J}{k}g*C$ and the latent heat of fusion for water is $330k\frac{J}{k}g$ determine the original mass of the ice chips.