Find initial temp. of alcohol when copper and aluminum are added

[nlingraham]

*Messed up title, should have been find initial temp of copper*

Homework Statement

8.00 g of aluminum at 200 °C and 18.0 g of copper are dropped into 50.0 cm³ of ethyl alcohol at 15 °C. The temperature quickly comes to 26.0 °C. What was the initial temperature of the copper?

Density of ethyl alcohol = .789 g/ml

mass of ethyl alcohol = 39.45 g, .03495 kg

mass of copper = .018 kg

mass of aluminum = .008 kg

T_f = 299 K

T_{i, alum} = 473 K

T_{i, eth} = 288 K

c for aluminum = 900 J/kg*k

c for ethyl alcohol = 2400 J/kg*k

c for copper = 385 J/kg*k

Homework Equations

Q_a + Q_c + Q_e = m_ac_aΔT + m_ec_eΔT + m_cc_cΔT = 0

The Attempt at a Solution

Q_a + Q_c + Q_e = m_ac_aΔT + m_ec_eΔT + m_cc_cΔT = 0

=(.008)(900)(-174) + (.03945)(2400)(11) + (.018)(385)(299-Ti) = 0

Ti = 268.51 K or -4.5 °C

That's what I did, but it says not quite and tells to check for rounding errors. However, I didn't round anything until the very end, so I'm not quite sure where I went wrong. I also tried -4.494 but that was wrong too.

 

[TSny]

mass of ethyl alcohol = 39.45 g, .03495 kg

Could this be the error?

 

[nlingraham]

Well, I feel stupid now. thanks.

 

[TSny]

No need to worry. We all make slips like that. Hope it works out now.

 

[Nickie]

I would first check my calculations to make sure they are accurate. Rounding errors can occur at any step in the calculation, so it's important to double check each step. Additionally, I would check to see if there are any units that need to be converted or if there are any missing units in the equation.

I would also consider the specific heat capacity values used for each substance. Are they accurate and appropriate for this specific scenario? Are there any other factors that could have affected the temperature change, such as heat loss to the surroundings?

Finally, I would also consider the significant figures used in the given values. Are they appropriate for the level of accuracy required in this calculation? It's possible that the answer could be slightly different depending on the number of significant figures used.

In summary, as a scientist, I would carefully review my calculations, check for appropriate units and significant figures, and consider any other factors that may have affected the temperature change.