The energy given off by 300 grams of an alloy as it cools through 50°C raises the temperature of 300 grams of water from 30°C to 40°C. The specific heat of the alloy (in cal/g C ) is:

i know Q=CpM(delta T)

but what is what?

Heat lost=heat gained

300*c*50=300*4.18*10

In the equation Q=CpM(delta T):

Q represents the amount of energy given off by the alloy as it cools.
Cp represents the specific heat capacity of the alloy.
M represents the mass of the alloy.
(delta T) represents the change in temperature of the alloy.

To solve for Cp, let's plug in the given values:
Q = unknown (we're trying to find Cp)
Cp = unknown
M = 300 grams (mass of the alloy)
(delta T) = -50°C (as the alloy cools from a higher temperature to a lower temperature)

We also know that the Q value from the alloy's cooling is the same as the Q value absorbed by the water as it heats up.

Q = CpwM(delta T)

In this equation:
Q represents the amount of energy absorbed by the water as it heats up.
Cpw represents the specific heat capacity of water.
M represents the mass of the water.
(delta T) represents the change in temperature of the water.

Let's plug in the given values for the water:
Q = Q (same as in the alloy equation)
Cpw = 1 cal/g °C (specific heat capacity of water)
M = 300 grams (mass of the water)
(delta T) = 10°C (temperature change of the water)

Now we can set up and solve the equation:

Q = CpM(delta T) (for the alloy)
Q = CpwM(delta T) (for the water)

Since Q is the same for both equations, we can set the two equations equal to each other:

CpM(delta T) = CpwM(delta T)

Cancel out the M and delta T terms:

Cp = Cpw

Therefore, the specific heat capacity of the alloy is the same as the specific heat capacity of water, which is 1 cal/g °C.

To use the formula Q = Cp * M * (delta T), we need to understand the variables:

Q represents the energy transferred or exchanged, usually measured in calories (cal).
Cp refers to the specific heat capacity of the material, which is the amount of energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius (cal/g °C).
M represents the mass of the material in grams.
(delta T) is the change in temperature, measured in degrees Celsius.

Now, let's apply this formula to the given question:

We have 300 grams of an alloy, so M = 300g.
The temperature change of the alloy is from an unknown initial temperature to 50°C, so (delta T) = 50°C - unknown initial temperature.
The energy transferred (Q) is the same as the energy gained by the water.
We have 300 grams of water, so M = 300g.
The temperature change of the water is from 30°C to 40°C, so (delta T) = 40°C - 30°C = 10°C.

Now we can set up the equation and solve for Cp:

Q (alloy) = Q (water)
Cp (alloy) * M (alloy) * (delta T) (alloy) = Cp (water) * M (water) * (delta T) (water)

Cp (alloy) * 300g * ((50°C - unknown initial temperature) = Cp (water) * 300g * 10°C

Simplifying the equation:

Cp (alloy) * (50°C - unknown initial temperature) = Cp (water) * 10°C

Now, without knowing the initial temperature, we cannot solve this equation directly. Therefore, we need additional information to find the specific heat capacity of the alloy.

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