The Ice Sculptor's Dilemma · AI Generator #GEN-5F123DC4

Physics · thermodynamics

Problem

An ice sculptor works in a studio where the ambient temperature is

20°\text{C}

. She has a large block of ice at

-10°\text{C}

with mass

m = 50\;\text{kg}

. To prevent the ice from melting while she works, she places it in an insulated container and adds dry ice (solid

\text{CO}_2

) which sublimes at

-78°\text{C}

. The dry ice sublimes and the cold

\text{CO}_2

gas absorbs heat from the ice block, keeping it frozen. If she adds

M = 2.0\;\text{kg}

of dry ice to the container, what is the final temperature of the ice block after thermal equilibrium is reached? Assume the

\text{CO}_2

gas eventually reaches thermal equilibrium with the ice and that no heat is exchanged with the surroundings. Given data: - Specific heat of ice:

c_{\text{ice}} = 2100\;\text{J/(kg·K)}

- Specific heat of

\text{CO}_2

gas:

c_{\text{CO}_2} = 840\;\text{J/(kg·K)}

- Latent heat of sublimation of dry ice:

L = 571{,}000\;\text{J/kg}