Solving for Entropy Change: Copper & Water

• MeliMo
In summary, to find the entropy change of the system, we first determine the final equilibrium temperature using the equation [(m1*c1*T1) + (m2*c2*T2)] / [(m1*c1) + (m2*c2)]. Then, using the equation dQ = m*c*dT, we can calculate the change in entropy for both the copper block and the water. The total change in entropy will be the sum of these two values. It is important to note that the total change in entropy must be greater than or equal to zero in order to obey the laws of thermodynamics.

Homework Statement

A 500 g copper block at 80 C is dropped into 1.0 kg of water at 10 C. Find the entropy change of the system.

Homework Equations

dS= integral of dQ/T

The Attempt at a Solution

I found that the final equilibrium temperature is 290 K using the equation
[(m1*c1*dT1) + (m2*c2*dT2)]/ [(m1*c1) + (m2*c2)]
I know that this is correct, but I'm not sure what to do from here. I know that this is Tf, but what do I use as Ti for the integral, the temperature of the block or the water? And which equation do I integrate to find the entropy in this case (What is the equation for Q)?

Well, not sure why you wrote dT1 and dT2 in the equation. But you are correct if you meant:
$$T_f = \left(m_1 c_1 T_1 + m_2 c_2 T_2\right)/\left(m_1 c_1 + m_2 c_2\right)$$

You also know that $$dQ = m\cdot c\cdot dT$$ but forgot to mention it in your list of equations. Knowing this and that
$$\Delta S = \int_{T_i}^{T_f}dQ/T$$
you can solve for the change in entropy, $$\Delta S$$, for both systems. The total change in entropy will just be the sum of the two values.

P.S.: Be careful with units. And be sure the total change in entropy is greater than or equal to zero, we don't want to be breaking any laws here :)

Thank You!

1. What is the equation for calculating entropy change?

The equation for calculating entropy change is ΔS = Q/T, where ΔS represents the change in entropy, Q represents the heat transferred, and T represents the temperature in Kelvin.

2. How do you determine the change in entropy for a system?

The change in entropy for a system can be determined by calculating the difference between the final and initial entropies of the system. This can be done using the equation ΔS = Sf - Si, where Sf is the final entropy and Si is the initial entropy.

3. Can entropy change be negative?

Yes, entropy change can be negative. This indicates that the system has become more ordered and has a lower level of disorder or randomness.

4. How does copper and water affect entropy change?

Copper and water can affect entropy change by transferring heat energy. When copper and water are in contact, heat will flow from the higher temperature substance (copper) to the lower temperature substance (water). This transfer of heat will result in an increase in the entropy of the system.

5. What factors can influence the change in entropy for a system?

The change in entropy for a system can be influenced by factors such as temperature, pressure, and the number of particles in the system. Additionally, the physical and chemical properties of the substances involved can also affect the change in entropy.