# Finding Initial Temperature Entropy and Heat Exchange

• Luke Strand
In summary, the problem involves finding the initial temperature of water when a 2.45 kg aluminium pan at 155 C is plunged into 3.58 kg of water and the entropy change of the system is 162 J/k. Using the equations Q = mcΔT, ΔS=mcln(T_2/T_1), and Q_water + Q_Aluminium = 0, and the specific heat capacities of water and aluminium, the initial temperature of the water can be solved for. However, after multiple attempts, the correct answer of 16 degrees C cannot be obtained. It may be helpful to try substituting 16 C into the equations to see if it yields a solution.
Luke Strand

## Homework Statement

A 2.45 kg aluminium pan at 155 C is plunged into 3.58 kg of water. If the entropy change of the system is 162 J/k, what is the initial temperature of the water?

## Homework Equations

Q = mcΔT ΔS=mcln(T_2/T_1) Q_water + Q_Aluminium = 0
c water = 4184 J/kg*K c aluminium = 900 J/kgK
3. Attempted Solutions
T_i Aluminum = 155
T_f is the same for the water and aluminium
T_i where T_i is the initial temperature of the water.
162 = (3.58)(4184)(ln(T_f/T_i) + (2.45)(900)ln((T-f)/(428))
(3.54)(4814)(T_f-T_i) + (2.45)(900)(T_f - 428)= 0

After solving this system of equations multiple times I can't seem to get the correct answer. The answer is 16 degrees C but I am not sure how to get there.

Luke Strand said:

## Homework Statement

A 2.45 kg aluminium pan at 155 C is plunged into 3.58 kg of water. If the entropy change of the system is 162 J/k, what is the initial temperature of the water?

## Homework Equations

Q = mcΔT ΔS=mcln(T_2/T_1) Q_water + Q_Aluminium = 0
c water = 4184 J/kg*K c aluminium = 900 J/kgK
3. Attempted Solutions
T_i Aluminum = 155
T_f is the same for the water and aluminium
T_i where T_i is the initial temperature of the water.
162 = (3.58)(4184)(ln(T_f/T_i) + (2.45)(900)ln((T-f)/(428))
(3.54)(4814)(T_f-T_i) + (2.45)(900)(T_f - 428)= 0

After solving this system of equations multiple times I can't seem to get the correct answer. The answer is 16 degrees C but I am not sure how to get there.
Your setup is correct. Please show us what you did in attempting to solve the equations. Did you try substituting 16 C into the equations?

## 1. What is the formula for finding initial temperature?

The formula for finding initial temperature is T(initial) = T(final) - (Q/mc), where T is temperature, Q is heat exchange, m is mass, and c is specific heat capacity.

## 2. How is entropy related to heat exchange?

Entropy is a measure of the disorder or randomness in a system. Heat exchange can increase the entropy of a system by increasing the disorder of the molecules and their movement.

## 3. What is the difference between heat and temperature?

Heat is a form of energy that is transferred between objects due to a temperature difference. Temperature is a measure of the average kinetic energy of the molecules in an object.

## 4. Can initial temperature be negative?

Yes, initial temperature can be negative. This indicates that the initial state of the system is colder than the final state, and heat must be added to the system to reach the final temperature.

## 5. What are the units for heat exchange?

The units for heat exchange are joules (J) in the International System of Units (SI).

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