Solving Algebraically for T2: Q Lost = Q Gained

  • Thread starter Thread starter Soliloquy12
  • Start date Start date
  • Tags Tags
    Lost
Click For Summary
SUMMARY

The discussion focuses on solving for the final temperature T2 in a heat transfer problem using the equation QLost = QGained. The initial values provided are T1C = 63°C, T1H = 79.5°C, MCW = 8.63g, and MBW = 36.48g. The user derived the equation T2 = (MCW*T1C + MBW*T1H) / (MBW + MCW) but encountered discrepancies in the calculated values of T2, yielding 123.66°C and 76.34°C. Participants emphasized the need for clarity in calculations and suggested checking for algebraic errors, as the final temperature should logically fall between the two initial temperatures.

PREREQUISITES
  • Understanding of heat transfer principles, specifically QLost and QGained.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of specific heat capacity concepts.
  • Basic skills in unit conversion and temperature measurement.
NEXT STEPS
  • Review the principles of heat transfer and the conservation of energy.
  • Practice algebraic manipulation of equations in thermodynamics.
  • Learn about specific heat capacities and their role in temperature calculations.
  • Explore common mistakes in solving heat transfer problems and how to avoid them.
USEFUL FOR

Students studying thermodynamics, educators teaching heat transfer concepts, and anyone involved in solving algebraic equations related to temperature changes in physical systems.

Soliloquy12
Messages
2
Reaction score
0

Homework Statement



Solve algebraically for T2 then find T2.

T1C=63 Celsius
T1H=79.5 Celsius
MCW=8.63g
MBW=36.48g

Homework Equations



QLost = QGained

-mbwcw(T2-T1H) = mcwcw(T2-T1C)


The Attempt at a Solution



Trying to solve algebraically I arrived at:

T2 = mcwt1C+mbwt1h/(mbw+mcw)

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!
 
Physics news on Phys.org
Soliloquy12 said:
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.
 
Yes sorry i meant degrees celsius. I substitutted the values into the initial "long" equation when I got 123.66 degrees celsius.
 
Soliloquy12 said:
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?
 
Soliloquy12 said:

Homework Statement





-mbwcw(T2-T1H) = mcwcw(T2-T1C)


The Attempt at a Solution



Trying to solve algebraically I arrived at:

T2 = mcwt1C+mbwt1h/(mbw+mcw)

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.
 

Similar threads

Replies
40
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
13
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
9K
  • · Replies 6 ·
Replies
6
Views
1K
Replies
2
Views
8K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 13 ·
Replies
13
Views
4K