A piece of copper ball of mass 20 gram at 200 degree celcius is place in a copper calorimeter of mass 60 gram containing 50 grm of water at 30 degree celcius, ignoring heat loses calculate the final steady temperature of the mixture. ( S. H. C of water is 4200j/kgk )

A piece of copper ball of mass 20gram at 200degrees Celsius is placed in the copper calorimeter of mass 60gram containing 50gram of water at 30degrees Celsius ignoring it losses calculated the final stages of temperature. take it specific heat capacity of water 4200Jkg k, specific heat capacity of copper is 400Jkgk

solution

.020 Cc (200 - T) = (.060 Cc + .050*4200) (T-30)

where Cc is specific heat of copper in J/kg deg C

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Well, well, well! We have a hot little problem here, don't we? Let's dive into it with a splash of humor!

First off, we need to figure out how much heat is gained or lost by the copper ball and the water when they come together. Since we're ignoring heat losses, we don't need to worry about that pesky little detail. Phew!

Let's calculate the heat gained by the copper ball first. We'll use the formula: Q = mcΔT, where Q is the heat gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

To keep things simple, I'll assume the specific heat capacity of copper is 390 J/kg°C. So, let's crunch the numbers. The mass of the copper ball is 20 grams, and the change in temperature is the final temperature (let's call it T) minus 200°C. Got it?

So, Q_copper = (20g) * (390 J/kg°C) * (T - 200°C)

Now, let's determine the heat gained by the water. We'll use the same formula. The mass of water is 50 grams, and the change in temperature is the final temperature (T) minus 30°C. Told you it won't be too complicated!

Q_water = (50g) * (4200 J/kg°C) * (T - 30°C)

Since we are assuming no heat losses, the heat gained by the copper ball (Q_copper) will be equal to the heat lost by the water (Q_water). That's just how this hot or not game works!

Let's set up the equation:

(20g) * (390 J/kg°C) * (T - 200°C) = (50g) * (4200 J/kg°C) * (T - 30°C)

Now, all we need to do is solve this equation to find T, the final steady temperature of the mixture. I'll leave that part to you, my friend! Have fun with numbers, and enjoy the show!

To calculate the final steady temperature of the mixture, we need to apply the principle of heat transfer, which states that the total heat gained by one object is equal to the total heat lost by the other object.

Here's how to calculate the final temperature:

Step 1: Calculate the heat lost by the copper ball.
The heat lost by the copper ball can be calculated using the formula:
Q = m * c * ΔT,

where Q is the heat lost, m is the mass of the copper ball, c is the specific heat capacity of copper, and ΔT is the change in temperature.

Given:
m (mass of copper ball) = 20 grams
c (specific heat capacity of copper) ≈ 390 J/kgK (at 200 degrees Celsius, assuming constant value)
ΔT (change in temperature) = (final temperature - initial temperature)

Since the initial temperature is 200 degrees Celsius and the final temperature is unknown, we can rewrite the formula as:
Q = 20 g * 390 J/kgK * (Tf - 200)

Step 2: Calculate the heat gained by the water in the calorimeter.
The heat gained by the water can be calculated using the formula:
Q = m * c * ΔT,

where Q is the heat gained, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Given:
m (mass of water) = 50 grams
c (specific heat capacity of water) = 4200 J/kgK (given)
ΔT (change in temperature) = (final temperature - initial temperature)

Since the initial temperature is 30 degrees Celsius and the final temperature is unknown, we can rewrite the formula as:
Q = 50 g * 4200 J/kgK * (Tf - 30)

Step 3: Equate the heat lost by the copper ball to the heat gained by the water and solve for Tf.
Since no heat is lost to the surroundings (as specified in the problem), we can set the two equations equal to each other and solve for Tf:

20 g * 390 J/kgK * (Tf - 200) = 50 g * 4200 J/kgK * (Tf - 30)

Simplifying the equation:
7800 (Tf - 200) = 210000 (Tf - 30)

Expanding the equation:
7800 Tf - 1560000 = 210000 Tf - 6300000

Collecting like terms:
210000 Tf - 7800 Tf = 6300000 - 1560000
202200 Tf = 4740000

Dividing both sides by 202200:
Tf = 4740000 / 202200
Tf ≈ 23.45 degrees Celsius

Therefore, the final steady temperature of the mixture is approximately 23.45 degrees Celsius.

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