Thermodynamics: Solving for Initial Temperature of Copper in Ethanol Solution

[eliassiguenza]

Homework Statement

11 grams of Aluminium at 200 degrees Celsius and 19 grans of Copper are dropped into 49 cubic centimetres of ethanol at 15 Degrees Celsius, The temperature Quickly becomes 28 Deegres Celsuis.

What was the initial temperature of copper?

Homework Equations

Q= c dT

The Attempt at a Solution

I am very lost.. please help

 

[edgepflow]

This is a calorimetry problem.

Cast your formula in the following form: Q = m cp (Tf - To). Balance heat loss and heat gained by all the components. And note all materials will have the same Tf.

 

[eliassiguenza]

ok so what i did was to find Q value for Ethanol and Aluminium

Ethanol density = .79 g/ cm3 in 49 cm3 = 0.0387 kg
Q Al = 0.011kg * (900 J /kg K) * (473.15K - 301.15K)
Q Eth= 0.0387kg (2400J/kg K) * (301.15K- 288.15K)
Q Cu = 0.019kg * (385 j /Kg K) * (301.15 - ?)

am I going well ?

 

[Redbelly98]

Looks good so far.

 

[rwisz]

I would approach this problem by first identifying the relevant equations and variables involved in thermodynamics. In this case, the equation Q=cdT, where Q represents heat, c represents specific heat capacity, and dT represents the change in temperature, will be useful in solving for the initial temperature of copper.

Next, I would use the given information to set up and solve the necessary equations. The total heat (Q) in the system can be calculated by adding the heat gained by the ethanol and the heat gained by the copper. This can be represented as:

Q = (m1c1dT1) + (m2c2dT2)

Where m represents mass and c represents specific heat capacity. We know the mass and specific heat capacity of ethanol (m1 and c1) and the initial and final temperatures of both the ethanol and copper (dT1 and dT2). We are trying to solve for the initial temperature of copper (dT1).

We can rearrange the equation to solve for dT1:

dT1 = (Q - m2c2dT2) / (m1c1)

Substituting in the known values, we get:

dT1 = (49 cm^3 * 0.789 g/cm^3 * 2.44 J/gK * (28°C - 15°C) - 19 g * 0.385 J/gK * (28°C - 200°C)) / (11 g * 0.903 J/gK)

Simplifying, we get:

dT1 = 3.38°C

Therefore, the initial temperature of copper was 3.38°C.