a 0.15 kg sample of Alloy is heated 540°C. it is then quickly placed in 400 g of H2O at 10°C which is contain in a 200 g aluminum cup. the final temperature of the mixture is 20. 5 °C. calculate the specific heat of alloy.

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To calculate the specific heat of the alloy, we need to use the principle of heat transfer. The heat gained by the alloy equals the heat lost by the water. The formula for this principle is:

Heat gained by alloy = Heat lost by water

The heat gained by the alloy can be calculated using the formula:

Q1 = m1 * c1 * ΔT1

where:
Q1 is the heat gained by the alloy,
m1 is the mass of the alloy (0.15 kg),
c1 is the specific heat of the alloy (unknown), and
ΔT1 is the change in temperature of the alloy (20.5°C - 540°C).

The heat lost by the water can be calculated using the formula:

Q2 = m2 * c2 * ΔT2

where:
Q2 is the heat lost by the water,
m2 is the mass of the water (400 g),
c2 is the specific heat of water (4.18 J/g°C), and
ΔT2 is the change in temperature of the water (20.5°C - 10°C).

Since there is no heat exchanged with the aluminum cup, we do not need to consider it in this calculation.

Now, let's plug in the given values into the equations:

Q1 = m1 * c1 * ΔT1
Q1 = 0.15 kg * c1 * (20.5°C - 540°C)
Q1 = -78.75 kg·°C * c1

Q2 = m2 * c2 * ΔT2
Q2 = 400 g * 4.18 J/g°C * (20.5°C - 10°C)
Q2 = 400 g * 4.18 J/g°C * 10.5°C
Q2 = 1746 J * 10.5°C

Now we equate the heat gained by the alloy to the heat lost by the water:

Q1 = Q2

-78.75 kg·°C * c1 = 1746 J * 10.5°C

Now we solve for c1:

c1 = (1746 J * 10.5°C) / -78.75 kg·°C

By performing the calculation, we find that the specific heat of the alloy is approximately -232 J/kg·°C.