Question

A 0.5 kg piece of ice at -10 degrees Celsius is placed in 3 kg of water at 20 degrees Celsius. What temperature will the mixture finally be at? Consider that: cA=4186 J/kg°C and cH=2100 J/kg°C

271

likes
1354 views

Answer to a math question A 0.5 kg piece of ice at -10 degrees Celsius is placed in 3 kg of water at 20 degrees Celsius. What temperature will the mixture finally be at? Consider that: cA=4186 J/kg°C and cH=2100 J/kg°C

Expert avatar
Corbin
4.6
56 Answers
Step 1: Calculate the heat required to raise the temperature of ice from -10°C to 0°C.

The heat (Q) required to raise the temperature of the ice can be calculated using the formula:

Q = mcΔT

Given: mass of ice (m) = 0.5 kg, specific heat of ice (cA) = 2100 J/kg°C, initial temperature (Ti) = -10°C, final temperature (Tf) = 0°C

Q = 0.5 \times 2100 \times (0 - (-10))
Q = 0.5 \times 2100 \times 10 = 10500 J

Step 2: Calculate the heat required to melt the ice at 0°C.

The heat (Q) required to melt the ice can be calculated using the formula:

Q = mL
step 2.1:calculate the heat required to raise water(from ice) to final temperature
Q=0.5*4186*x


Given: latent heat of fusion of ice (L) = 334000 J/kg

Q = 0.5 \times 334000 = 167000 J

Step 3: Calculate the heat required to raise the temperature of the water from 20°C to the final temperature.

The heat (Q) required to raise the temperature of water can be calculated using the formula:

Q = mcΔT

Given: mass of water (m) = 3 kg, specific heat of water (cH) = 4186 J/kg°C, initial temperature (Ti) = 20°C, final temperature (Tf) = x°C

Q = 3 \times 4186 \times (x - 20)

Step 4: The total heat added to the system must be equal to zero for the final temperature to be reached.

10500+167000+0.5\times4186\times x+3\times4186\times(x-20)=0

Solving the equation gives:


177500+14651x-251160=0



14651x=73660

x ≈ 5°C

Therefore, the final temperature of the mixture will be approximately 5°C.

\textbf{Answer:} The final temperature of the mixture will be approximately 5°C.

Frequently asked questions (FAQs)
Question: What is the result of multiplying two vectors, 𝐴 = [2, 3] and 𝐵 = [4, 5]?
+
Question: What is the slope of a line passing through the points (2, 3) and (5, 9)?
+
What is the congruence rule for triangles when two sides and the included angle are equal?
+
New questions in Mathematics
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
3(2+x)-2(2x+6)=20-4x
Jose bought 3/4 of oil and his sister bought 6/8, which of the two bought more oil?
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
3x+5y=11 2x-3y=1
Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.
Suppose the horses in a large they will have a mean way of 818 pounds in a variance of 3481. What is the probability that the mean weight of the sample of horses with differ from the population mean by more than 18 pounds is 34 horses are sampled at random from the stable.
224 × (6÷8)
Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?
A study reports the following final notation: F (3, 32) = 9.50, p < .05. How many total participants were involved in this study? Group of answer choices 34 32 36
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
At the dance there are 150 boys the rest are girls. If 65% are girls what is the total amount in the room
Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.
Nancy is a waitress at Seventh Heaven Hamburgers. She wants to estimate the average amount each table leaves for a tip. A random sample of 5 groups was taken and the amount they left for a tip (in dollars) is listed below: $11.00 $8.00 $6.00 $3.00 $7.00 a.) Find a 90% confidence interval for the average amount left by all groups. (*round to the nearest cent*) $ < μ < $ b.) If the sample size were larger, with everything else remaining the same, would the margin of Error increase or decrease? Decrease Increase c.) If the Confidence level were 95% instead of 90%, would the range (size) of the Confidence Interval be larger or smaller? Larger Smaller
Find the vertex F(x)=x^2-10x
A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?
Oi👋🏻 Toque em "Criar Nova Tarefa" para enviar seu problema de matemática. Um dos nossos especialistas começará a trabalhar nisso imediatamente!
What is the percentage of nitrogen abundance in copper dinatrate Cu(NO3)2
Convert (324)𝑓𝑖𝑣𝑒 into base-ten
Beren spent 60% of the money in her piggy bank, and Ceren spent 7% of the money in her piggy bank to buy a joint gift for Deren, totaling 90 TL. In the end, it was observed that the remaining amounts in Ceren and Beren's piggy banks were equal. Therefore, what was the total amount of money that Beren and Ceren had initially? A) 120 B) 130 C) 150 D) 160 E) 180