For the first question: Calculate Initial Temp of Forging (76kg, 430J/(kg·°C))

[wlvanbesien]

At a fabrication plant, a hot metal forging has a mass of 76 kg and a specific heat capacity of 430 J/(kg · °C). To harden it, the forging is immersed in 710 kg of oil that has a temperature of 32°C and a specific heat capacity of 2900 J/(kg · °C). The final temperature of the oil and forging at thermal equilibrium is 46°C. Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.


(the sub 1 refers to the metal, the o refers to the oil)
what I assumed I would do for this is say:
$$m_{1}c_{1}T_{1}=m_{o}c_{o}(\Delta T_{o} - 46^o C)$$
then
$$T_{1}=\frac{m_{o}c_{o}(\Delta T_{o} - 46^o C)}{m_{1}c_{1}}$$

That, unfortunately, is wrong...
any help would be great ... this is due in an hour.

I also have a problem with this question:
A precious-stone dealer wishes to find the specific heat capacity of a 0.032 kg gemstone. The specimen is heated to 95.0°C and then placed in a 0.10 kg copper vessel that contains 0.083 kg of water at equilibrium at 25.0°C. The loss of heat to the external environment is negligible. When equilibrium is established, the temperature is 28.5°C. What is the specific heat capacity of the specimen?

for this one i used the same
$$c_{1}m_{1}\Delta T_{1}=c_{2}m_{2}\Delta T_{2}$$
formula, but it was wrong again... Am I even using the correct formula? Thanks!

 

[dextercioby]

For the first problem,u assumed wrongly that the temperature of the metal is kept constant at 46°...Redo the thinking.

Daniel.

 

[wais]

For the first question, the correct formula to use is the heat transfer equation, Q = mcΔT, where Q is the amount of heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. In this case, we want to find the initial temperature of the forging, so we can set up the equation as follows:

Q1 = Q2

(m1)(c1)(T1 - T2) = (m2)(c2)(T2 - Tfinal)

Where Q1 is the heat absorbed by the forging, Q2 is the heat released by the oil, and Tfinal is the final temperature of both the forging and the oil at thermal equilibrium.

Substituting the given values, we get:

(76 kg)(430 J/(kg·°C))(T1 - 46°C) = (710 kg)(2900 J/(kg·°C))(46°C - 32°C)

Solving for T1, we get an initial temperature of 128.4°C for the forging.

For the second question, the correct formula to use is the same heat transfer equation, but we need to account for the fact that the gemstone is heated and then placed in the copper vessel. So we can set up the equation as follows:

Q1 + Q2 = Q3

Where Q1 is the heat absorbed by the gemstone, Q2 is the heat absorbed by the copper vessel, and Q3 is the heat released by the gemstone and copper vessel to reach thermal equilibrium.

Substituting the given values, we get:

[(0.032 kg)(c1)(95.0°C - T1)] + [(0.10 kg)(387 J/(kg·°C))(T1 - 28.5°C)] = [(0.032 kg)(387 J/(kg·°C))(T1 - 28.5°C)]

Solving for c1, we get a specific heat capacity of 743.8 J/(kg·°C) for the gemstone.

Make sure to double check your calculations and units to avoid any errors. It's also helpful to label your variables clearly to avoid confusion. Good luck!