I need help on this question
79 g of water at 95 degree Celsius were added to tap water at 22 degree Celsius, and the Temperature of the mixture after all thermal energy transfer ended at 36 degree Celsius. What was the mass of the tap water?
(teacher's answer key : 412 grams)
Im not sure what I did wrong, but anyways here's my work
MCT=-MCT
Convert grams to KeloGrams
(0.079)(4.2x10^3)(95-36)=-(M)(4.2x10^3)(22-36)
get rid of (4.2x10^3) from both sides because it is the same. So...
(0.079)(95-36)=-(M)(22-36)
4.661=-(M)(-14)
4.661/-14 =-(M)
-0.33= -M
0.33 = M
This was apparently wrong.....where did I go wrong any help please?
I don't see an error. Lets do it my way:
The sum heats gained is zero.
79*c*(95-36)+M*c*(22-36)=0
M= 79g*59/14=333 grams.
The heat lost by the hot water equals the heat gained by the tap water. The hot water cools 59 C and the tap water warms up by 14 C.
79*59*C =M*14*C
The specific heat C cancels out.
M = (59/14)*79 grams
= 333 g = 0.333 kg
I agree with your answer.
okay thanks alot guyz!
To find the mass of the tap water, we can set up an equation using the principle of conservation of energy.
First, let's calculate the thermal energy gained by the water at 95 degrees Celsius:
Mass of water = 79 g
Specific heat capacity of water = 4.2 J/g°C
Change in temperature = 36°C - 95°C = -59°C
Thermal energy gained by the water = (Mass of water) × (Specific heat capacity of water) × (Change in temperature)
Thermal energy gained by the water = (79 g) × (4.2 J/g°C) × (-59°C)
Thermal energy gained by the water = -18713.4 J
Now, let's calculate the thermal energy lost by the tap water:
Mass of tap water = M
Specific heat capacity of water = 4.2 J/g°C
Change in temperature = 36°C - 22°C = 14°C
Thermal energy lost by the tap water = (Mass of tap water) × (Specific heat capacity of water) × (Change in temperature)
Thermal energy lost by the tap water = (M) × (4.2 J/g°C) × (14°C)
Thermal energy lost by the tap water = 58.8M J
Since the thermal energy gained by the water is equal to the thermal energy lost by the tap water, we can set up the equation:
Thermal energy gained = Thermal energy lost
-18713.4 J = 58.8M J
Solve for M:
M = (-18713.4 J) / (58.8 J/g)
M ≈ -317.9 g
The negative value indicates that there was an error in your calculations. The negative sign can be removed, as mass cannot be negative in this context.
Hence, the mass of the tap water is approximately 317.9 grams. This answer does not match the teacher's answer key of 412 grams, so it is possible that there may have been an error in the question or answer key.