## Provide a reasonable estimate of the cross-sectional area of this needle

The density of ice is 0.917 g/om’. The latent heat for melting ice is 33 1/g Let us model a sewing needle as a cylinder with a small diamcter. Provide a reasonable estimate of the cross-sectional area of this needle. Provide an estimate of the temperature of an ice cube just removed from the freezer of a standard refrigerator. Also provide a reasonable estimate of the force that a person would apply to this heedle if he or she attempted to push it into an ice cube. (a) (b) Using your numbers from pat ln), determine if the ice will melt under the tip of the needle as the person attempts to push it into the ice cube. (Recall dP/dT As AV)

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