A 50-g chunk of 80 degrees C iron is dropped into a cavity in a very large block of ice at 0 degrees C. Show that 5.5 g of ice will melt. (The specific heat capacity of iron is 0.11 cal / (g * degree C)).

Respuesta :

Answer:

5.5g of ice melts when a 50g chunk of iron at 80°C is dropped into a cavity

Explanation:

The concept to solve this problem is given by Energy Transferred, the equation is given by,

[tex]Q = mc\Delta T[/tex]

Where,

Q= Energy transferred

m = mass of water

c = specific heat capacity

[tex]\Delta T =[/tex] Temperature change (K or °C)

Replacing the values where mass is 50g and temperature is 80°C to 0°C we have,

[tex]Q = mc\Delta T[/tex]

[tex]Q = 50*0.11*(80-0)[/tex]

[tex]Q = 440cal[/tex]

Then we can calculate the heat absorbed by m grams of ice at 0°C, then

[tex]Q_2 = mL = 80*m[/tex]

How Q_1=Q_2, so

[tex]80m=440[/tex]

[tex]m=\frac{440}{80}[/tex]

[tex]m = 5.5g[/tex]

Then 5.5g of ice melts when a 50g chunk of iron at 80°C is dropped into a cavity

The mass of the ice that will melt is 5.5 g.

Heat capacity of water

The quantity of heat lost by the iron is determined using the following formula;

Heat lost by the iron

Q = mcΔT

Q = 50 x 0.11 x (80 -0)

Q = 440 cal

Heat gained by ice

The heat gained by ice is equal to heat lost by iron.

Heat gained by ice = m(80-0) = 440

m = 440/80

m = 5.5 g

Thus, the mass of the ice that will melt is 5.5 g.

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