Question #245458

512 g of an unknown metal at a temperature of 15oC is dropped into a 100 g aluminum container holding 325 g of water at 98oC. A short time later, the container of water and metal stabilizes at a new temperature of 78oC. Identify the metal.  


1
Expert's answer
2021-10-02T10:46:51-0400

Here we will apply the conservation of energy. It means heat gained by the metal = Heat lost by the water.

Heat gained by the metal = heat loss by water + calorie meter

Mass of metal (M1)=512g(M_1) = 512g

Mass of water (M2)=325g(M_2) = 325g

Initial temperature of the metal (T1)=15°C(T_1) = 15°C

Initial temperature of water (T2)=98°C(T_2) = 98°C

Final temperature of the mixture (T3)=78°C(T_3) = 78°C

Specific heat capacity of metal (C1)=?(C_1) = ?

Specific heat capacity of water (C2)=4.184J/g°C(C_2) = 4.184J/g°C

Heat loss by water = heat gain by the metal

M2C2(T2T3)=M1C1(T3T1)M_2C_2(T_2 - T_3) = M_1C_1(T_3 - T_1)

325×4.184×(9878)=512×C1×(7815)\Rightarrow 325 × 4.184 × (98 - 78) = 512 × C_1 × (78 - 15)

1359.8×20=512C1×63\Rightarrow 1359.8 × 20 = 512C_1 × 63

27196=32256C1\Rightarrow 27196 = 32256C_1

C1=27196/32256\Rightarrow C_1 = 27196 / 32256

C1=0.843J/g°C\Rightarrow C_1 = 0.843J/g°C

The specific heat capacity of the metal is 0.843J/g°C0.843J/g°C


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