Copper Block On Ice

Part of eval multi-llm branch, agent version multi-llm-servers · 2b11b97

Q. 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

24 checks, 1 agreed

draft 24: agreed

Latest draft

question.rb1 question :copper_block_on_ice do2   kind :numerical3   describes "A copper block of %{copper_mass} is heated in a furnace to a temperature of %{copper_temp} and then placed on a large ice block. Specific heat of copper = %{copper_specific_heat}; heat of fusion of water = %{fusion}. %{ice_melt}, in kg?"4   given copper_mass: "2.5 kg"5   given copper_temp: "500 °C"6   given copper_specific_heat: "0.39 J g-1 K-1"7   given fusion: "335 J g-1"8   asks ice_melt: "What is the maximum amount of ice that can melt"9 end

solution.rb1 solve :copper_block_on_ice, using: Calorimetry do2   objects :copper, :ice3 4   take copper_mass: copper.mass5   take copper_temp: copper.temperature_at_first6   take copper_specific_heat: copper.specific_heat_capacity7   take fusion: ice.latent_heat8 9   deduce_from "placed on a large ice block", ice.temperature_at_first => "0 °C"10   deduce_from "maximum amount of ice that can melt", copper.heat_to_warm => -(ice.heat_to_change_phase), copper.temperature_after => "0 °C", ice.temperature_after => "0 °C"11 12 13 14 15 16 17   18 19   ice_melt = ice.mass20   answer ice_melt:, in: "kg", figures: 221 22   conclusion "The copper cools to 0 °C, giving up heat that melts ice; the maximum ice melted is when all the copper's heat goes into melting."23 end

round 24

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Q. A copper block of 2.5 kg $m_{c} = 2.5$ kg is heated in a furnace to a temperature of 500 °C $T_{1,c} = 500$ °C and then placed on a large ice block $T_{1,i} = 0$ °C. Specific heat of copper = 0.39 J g⁻¹ K⁻¹ $s_{c} = 0.39$ J g⁻¹ K⁻¹; heat of fusion of water = 335 J g⁻¹ $L_{i} = 335$ J g⁻¹. What is the maximum amount of ice that can melt $T_{2,c} = 0$ °C, $T_{2,i} = 0$ °C, $Q_{c} = - Q_{L,i}$ , in kg?

The playground

Inputs

copper mass

m_{c}

2.5 kg

copper temp

T_{1,c}

500 °C

copper specific heat

s_{c}

0.39 J g⁻¹ K⁻¹

fusion

L_{i}

335 J g⁻¹

Outputs

ice melt

m_{i}

The solution

Solved with Calorimetry

Given

$m_{c} = 2.5$ kg
$T_{1,c} = 500$ °C
$s_{c} = 0.39$ J g⁻¹ K⁻¹
$L_{i} = 335$ J g⁻¹
$T_{1,i} = 0$ °C from “placed on a large ice block”
$T_{2,c} = 0$ °C from “maximum amount of ice that can melt”
$T_{2,i} = 0$ °C from “maximum amount of ice that can melt”
$Q_{c} = - Q_{L,i}$ from “maximum amount of ice that can melt”

Find $m_{i}$ .

Working

$T_{1,c} = 500$ °C $= 773.15$ K
$s_{c} = 0.39$ J g⁻¹ K⁻¹ $= 390$ J kg⁻¹ K⁻¹
$L_{i} = 335$ J g⁻¹ $= 335000$ J/kg
$T_{1,i} = 0$ °C $= 273.15$ K
$T_{2,c} = 0$ °C $= 273.15$ K
$T_{2,i} = 0$ °C $= 273.15$ K
heat warms a body(copper) $Q_{c} = m_{c} \cdot s_{c} \cdot (T_{2,c} - T_{1,c})$
$Q_{c} = 2.5 \cdot 390 \cdot (273.15 - 773.15)$
$Q_{c} = −487500$ J
maximum amount of ice that can melt $Q_{c} = - Q_{L,i}$
$(−487500) = - Q_{L,i}$
$Q_{L,i} = 487500$ J
heat changes a phase(ice) $Q_{L,i} = m_{i} \cdot L_{i}$
$487500 = m_{i} \cdot 335000$
$m_{i} = 1.455$ kg
$m_{i} \approx 1.5$ kgto 2 significant figures

Conclusion

The copper cools to 0 °C, giving up heat that melts ice; the maximum ice melted is when all the copper's heat goes into melting.

The Ruby

1question :copper_block_on_ice do2  kind :numerical3  describes "A copper block of %{copper_mass} is heated in a furnace to a temperature of %{copper_temp} and then placed on a large ice block. Specific heat of copper = %{copper_specific_heat}; heat of fusion of water = %{fusion}. %{ice_melt}, in kg?"4  given copper_mass: "2.5 kg"5  given copper_temp: "500 °C"6  given copper_specific_heat: "0.39 J g-1 K-1"7  given fusion: "335 J g-1"8  asks ice_melt: "What is the maximum amount of ice that can melt"9end

1solve :copper_block_on_ice, using: Calorimetry do2  objects :copper, :ice34  take copper_mass: copper.mass5  take copper_temp: copper.temperature_at_first6  take copper_specific_heat: copper.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", copper.heat_to_warm => -(ice.heat_to_change_phase), copper.temperature_after => "0 °C", ice.temperature_after => "0 °C"11121314151617  1819  ice_melt = ice.mass20  answer ice_melt:, in: "kg", figures: 22122  conclusion "The copper cools to 0 °C, giving up heat that melts ice; the maximum ice melted is when all the copper's heat goes into melting."23end

1play_with :copper_block_on_ice do2  title "Copper Block On Ice"3end

The laws

quantity	written	units	within	from
mass	$m$	kg	0 … ∞	Calorimetry
specific heat capacity	$s$	J kg⁻¹ K⁻¹	—	Calorimetry
latent heat	$L$	J/kg	—	Calorimetry
temperature at first	$T_{1}$	K	—	Calorimetry
temperature after	$T_{2}$	K	—	Calorimetry
heat to warm	$Q$	J	—	Calorimetry
heat to change phase	$Q_{L}$	J	—	Calorimetry
heat taken in	$Q_{in}$	J	—	Calorimetry
heat to warm of ground	$Q_{g}$	J	—
mass of ground	$m_{g}$	kg	0 … ∞
specific heat capacity of ground	$s_{g}$	J kg⁻¹ K⁻¹	—
temperature after of ground	$T_{2,g}$	K	—
temperature at first of ground	$T_{1,g}$	K	—
heat to warm of copper	$Q_{c}$	J	—
mass of copper	$m_{c}$	kg	0 … ∞
specific heat capacity of copper	$s_{c}$	J kg⁻¹ K⁻¹	—
temperature after of copper	$T_{2,c}$	K	—
temperature at first of copper	$T_{1,c}$	K	—
heat to warm of ice	$Q_{i}$	J	—
mass of ice	$m_{i}$	kg	0 … ∞
specific heat capacity of ice	$s_{i}$	J kg⁻¹ K⁻¹	—
temperature after of ice	$T_{2,i}$	K	—
temperature at first of ice	$T_{1,i}$	K	—
heat to change phase of ground	$Q_{L,g}$	J	—
latent heat of ground	$L_{g}$	J/kg	—
heat to change phase of copper	$Q_{L,c}$	J	—
latent heat of copper	$L_{c}$	J/kg	—
heat to change phase of ice	$Q_{L,i}$	J	—
latent heat of ice	$L_{i}$	J/kg	—
heat taken in of ground	$Q_{in,g}$	J	—
heat taken in of copper	$Q_{in,c}$	J	—
heat taken in of ice	$Q_{in,i}$	J	—

Q_{b} = m_{b} \cdot s_{b} \cdot (T_{2,b} - T_{1,b})

heat warms a body

Q_{L,b} = m_{b} \cdot L_{b}

heat changes a phase

Q_{in,b} = Q_{b} + Q_{L,b}

heat taken in warms and changes phase

Q_{g} = m_{g} \cdot s_{g} \cdot (T_{2,g} - T_{1,g})

heat warms a body(ground)

Q_{c} = m_{c} \cdot s_{c} \cdot (T_{2,c} - T_{1,c})

heat warms a body(copper)

Q_{i} = m_{i} \cdot s_{i} \cdot (T_{2,i} - T_{1,i})

heat warms a body(ice)

Q_{L,g} = m_{g} \cdot L_{g}

heat changes a phase(ground)

Q_{L,c} = m_{c} \cdot L_{c}

heat changes a phase(copper)

Q_{L,i} = m_{i} \cdot L_{i}

heat changes a phase(ice)

Q_{in,g} = Q_{g} + Q_{L,g}

heat taken in warms and changes phase(ground)

Q_{in,c} = Q_{c} + Q_{L,c}

heat taken in warms and changes phase(copper)

Q_{in,i} = Q_{i} + Q_{L,i}

heat taken in warms and changes phase(ice)

Q_{c} = - Q_{L,i}

maximum amount of ice that can melt