If 200g of water at 20˚ C is combined with 100g of water at 80˚ C, what is the final temperature of the 200g of water?
How do you do this??? steps by steps??
The final temperature of the 200 g of water will be the same as that of the 100g of hot water that was added. That is when thermal equilibrium exists.
At the final temperature T, the heat gained by the initially cold water will equal the heat lost by the hot water.
C*200g*(T-20) = C*100g*(80-T)
The specific heat C cancels out.
Solve for T, the final equilibrium temperature
2(T-20) = 80-T
3T = 120
T = 40 C
To find the final temperature of the water when 200g at 20˚C is combined with 100g at 80˚C, you can use the principle of heat transfer.
Here are the steps to calculate the final temperature:
Step 1: Calculate the heat absorbed or released by each water sample using the formula Q = mcΔT, where Q is the heat transfer, m is the mass of water, c is the specific heat capacity of water (assumed to be 1 calorie/gram°C), and ΔT is the change in temperature.
For the 200g of water:
Q1 = m1 * c * ΔT1
Q1 = 200g * 1 cal/g°C * (T - 20°C)
For the 100g of water:
Q2 = m2 * c * ΔT2
Q2 = 100g * 1 cal/g°C * (T - 80°C)
Step 2: Since the total heat lost by one water sample is equal to the total heat gained by the other sample (assuming no heat is lost to the surroundings), set the two equations equal to each other:
Q1 = Q2
200g * 1 cal/g°C * (T - 20°C) = 100g * 1 cal/g°C * (T - 80°C)
Step 3: Simplify and solve for T (the final temperature):
200(T - 20) = 100(T - 80)
200T - 4000 = 100T - 8000
100T = 4000
T = 40°C
Therefore, the final temperature of the 200g of water is 40°C.
To find the final temperature of the two water samples after they are combined, you can use the principle of energy conservation, specifically the principle of heat transfer.
Here are the step-by-step instructions to solve the problem:
Step 1: Understand the principle of heat transfer
Heat transfer between two bodies can be calculated using the formula Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
Step 2: Calculate the heat transfer for each water sample
Calculate the heat transfer for the first water sample (200g at 20˚C) using the formula Q1 = m1c1ΔT1. Since the initial temperature is 20˚C, the change in temperature (ΔT1) would be the final temperature minus the initial temperature.
Step 3: Calculate the heat transfer for the second water sample
Calculate the heat transfer for the second water sample (100g at 80˚C) using the formula Q2 = m2c2ΔT2. Since the initial temperature is 80˚C, the change in temperature (ΔT2) would be the final temperature minus the initial temperature.
Step 4: Set up the equation for energy conservation
According to the principle of energy conservation, the total heat transfer for both water samples must be equal to zero (Q1 + Q2 = 0).
Substitute the formulas for Q1 and Q2 into the equation: m1c1ΔT1 + m2c2ΔT2 = 0.
Step 5: Substitute the given values
Substitute the given values into the equation from the problem:
200g * c1 * (final temperature - 20˚C) + 100g * c2 * (final temperature - 80˚C) = 0
Step 6: Solve the equation
Simplify the equation and solve for the final temperature. You will have an equation with only one unknown, the final temperature.
Step 7: Calculate the final temperature
Plug in the values for c1 and c2, which are the specific heat capacities for water. The specific heat capacity for water is approximately 4.18 J/g˚C.
By solving the equation, you will find the final temperature of the 200g of water after combining with the 100g of water at a higher temperature.
Please note that the specific heat capacity values used in this explanation are approximate. Always refer to more precise values or consult a reference book for accurate calculations.