A few questions about water pressure, temp, and sound

[Scirel]

OK.

I have done most of them correctly on my own, I need 2 checked and help with one:

Check:

A sound source emits sounds of frequency 210 Hz that travel through still air at 340 m/s. The source moves away from the stationary listener at 80 m/s. Find the wavelength of the sound waves between the source and the listener.

I got Wavelength =2m

A small immersion heater is rated at 380 Watts. Estimate how long it will take to heat a cup of soup (assume this is 240g of water) from 23oC to 56oC

I got t=87.2451s


Now I need help with this one:

A 3.8 kg block of copper at a temperature of 79oC is dropped into a bucket containing a mixture of ice and water whose total mass is 1.2 kg. When thermal equilibrium is reached the temperature of the water is 8°C. How much ice was in the bucket before the copper block was placed in it?
(Neglect the heat capacity of the bucket.)

I know heat gained=heat lost, so:

3.8*(79-8)*387(heat capacity of copper) = ?

I don`t know how to treat the mixture of ice and water. can someone please help me?

 

[Scirel]

Please! I truly need help before 10:00!

 

[thepatientmental]

Sure, I can help you with this problem. Let's break it down step by step.

First, let's calculate the heat lost by the copper block as it cools down from 79°C to 8°C. We can use the formula Q = mcΔT, where Q is the heat lost, m is the mass of the copper block, c is the specific heat capacity of copper, and ΔT is the change in temperature.

So, Q = (3.8 kg)(387 J/kg°C)(79°C-8°C) = 106,666.8 J

Next, we need to calculate the heat gained by the ice and water as they warm up from 0°C to 8°C. Since we know that the final temperature of the mixture is 8°C, we can use the formula Q = mcΔT again, but this time we need to use the specific heat capacity of water. The total mass of the ice and water is 1.2 kg, so:

Q = (1.2 kg)(4186 J/kg°C)(8°C-0°C) = 40,224 J

Now, since we know that heat gained = heat lost, we can set these two equations equal to each other and solve for the mass of ice in the bucket.

106,666.8 J = 40,224 J + (m)(334 J/kg°C)(8°C-0°C)

Solving for m, we get m = 0.36 kg of ice.

Therefore, there was 0.36 kg of ice in the bucket before the copper block was placed in it. I hope this helps! Let me know if you need any further clarification.