Solving Algebraically for T2: Q Lost = Q Gained

[Soliloquy12]

Homework Statement

Solve algebraically for T2 then find T2.

T_1C=63 Celsius
T_1H=79.5 Celsius
M_CW=8.63g
M_BW=36.48g

Homework Equations

Q_Lost = Q_Gained

-m_bwc_w(T₂-T_1H) = m_cwc_w(T₂-T_1C)

The Attempt at a Solution

Trying to solve algebraically I arrived at:

T₂ = m_cwt_1C+m_bwt_1h/(m_bw+m_cw)

But when substituting the values I get T2 = 123.66J from the original equation and T2 = 76.34 when using the equation I derived from the original.

Can someone please show me where I am going wrong with the equation here?

Thanks!

 

[Doc Al]

But when substituting the values I get T2 = 123.66J from the original equation

What do you mean? How exactly did you get that result? (I assume that's the final temperature of some mixture, not an energy in Joules.)

and T2 = 76.34 when using the equation I derived from the original.

I didn't do the calculation, but if the problem is what I think it is, that sounds reasonable.

 

[Soliloquy12]

Yes sorry i meant degrees celsius. I substitutted the values into the initial "long" equation when I got 123.66 degrees celsius.

 

[Doc Al]

Yes sorry i meant degrees celsius. I substitutted the values into the initial "long" equation when I got 123.66 degrees celsius.

I still don't know what you mean. The initial "long" equation is the same equation that you rearranged to solve for T2. All you did was solve it algebraically--it's still the same equation.

Show exactly what you did. What values did you substitute?

 

[AEM]

Homework Statement

-m_bwc_w(T₂-T_1H) = m_cwc_w(T₂-T_1C)

The Attempt at a Solution

Trying to solve algebraically I arrived at:

T₂ = m_cwt_1C+m_bwt_1h/(m_bw+m_cw)

But when substituting the values I get T2 = 123.66J from the original equation and T2 = 76.34 when using the equation I derived from the original.

Can someone please show me where I am going wrong with the equation here?

Thanks!

First, I would suggest that you put parentheses around the two terms in your numerator for clarity and to prevent mistakes.

Second, I'm assuming that this problem involves adding something hot to something cool because you didn't really say. In problems such as that the final temperature will lie between the two starting temperatures. Therefore you should suspect that you made a simple algebraic error when you computed 123.66 degrees. As Dr AL indicated, without seeing the details of your calculation, one can't say more.