Part of eval multi-llm main, agent version f0f5267
A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then placed on a large ice block. Specific heat of copper = 0.39 J g⁻¹ K⁻¹; heat of fusion of water = 335 J g⁻¹. What is the maximum amount of ice that can melt, in kg?
expects 1.5 kg
draft 18: failed while solving — RuntimeError: no equation determines the mass of ice from what is known the engine knows: known: mass of block; temperature at first of block; specific heat capacity of block; latent heat of ice; temperature at first of ice; heat_warms_a_body(ice): heat to warm of ice == ((mass of ice * specific heat capacity of ice) * (temperature after of ice - temperature at first of ice)) — not yet known: heat to warm of ice; specific heat capacity of ice; temperature after of ice; heat_changes_a_phase(ice): heat to change phase of ice == (mass of ice * latent heat of ice) — not yet known: heat to change phase of ice
1solve :copper_block_on_ice, using: Calorimetry do2 objects :block, :ice34 take block_mass: block.mass5 take hot: block.temperature_at_first6 take copper_heat: block.specific_heat_capacity7 take fusion: ice.latent_heat89 deduce_from "placed on a large ice block", ice.temperature_at_first => "0 °C"10 deduce_from "maximum amount of ice that can melt", block.heat_to_warm => -(ice.heat_to_change_phase)1112 heat_released = block.heat_to_warm13 heat_absorbed = ice.heat_to_change_phase141516 ice_mass = ice.mass17 answer ice_mass:, in: "kg"1819 conclusion "The copper cools to the melting point of ice, giving up heat that melts ice; the maximum melt occurs when all the copper's heat goes into melting."20endRuntimeError: no equation determines the mass of ice from what is known
the engine knows: known: mass of block; temperature at first of block; specific heat capacity of block; latent heat of ice; temperature at first of ice; heat_warms_a_body(ice): heat to warm of ice == ((mass of ice * specific heat capacity of ice) * (temperature after of ice - temperature at first of ice)) — not yet known: heat to warm of ice; specific heat capacity of ice; temperature after of ice; heat_changes_a_phase(ice): heat to change phase of ice == (mass of ice * latent heat of ice) — not yet known: heat to change phase of ice