A 34 g glass thermometer reads 21.6°C before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 38.7°C. What was the original temperature of the water?
-.135(4186)(Tf-38.7)=.034(840)(Tf-21.6)
=-565.11Tf+21869.752=28.56Tf-616.896
solve for Tf
Tf= 37.88 degree celcius but its wrong please help!
thank you
m1•c1•(38.7-21.6) = m2•c2•(t-38.7)
m2 =ρ•V =1000• 135•10^-3•10^-3 =0.135 kg,
c1 =840 J/kg , c2 = 4180 J/kg.
t -38.7 = 0.034•840•17.1/0.135•4180 = 0.865 oC.
t = 38.7+ 0.865 =39.57oC
If no specific heat capacity of gladd
Well, well, well, looks like we have a temperature mystery here! Let me put on my detective hat and see if I can solve it for you.
First things first, let's examine the equation you've provided. It seems like a simple case of algebra. However, equations can sometimes be tricky, just like that clown who never stops juggling.
The equation you wrote is:
-.135(4186)(Tf-38.7) = .034(840)(Tf-21.6)
Now, let's simplify it step by step to avoid any confusion.
First, multiply everything inside the parentheses:
-565.11Tf + 23325.645 = 28.56Tf - 2896.16
Next, gather the variables on one side and the numbers on the other side:
-565.11Tf - 28.56Tf = -2896.16 - 23325.645
Combining like terms:
-593.67Tf = -26221.805
And finally, divide both sides by -593.67 to solve for Tf:
Tf = (-26221.805)/(-593.67)
Using our detective skills with a pinch of humor, we find that Tf is approximately equal to 44.11°C.
So, the original temperature of the water is around 44.11°C, not 37.88°C. Keep in mind that my calculations might be as questionable as a banana peel, so please double-check your work just to be sure. Now, go make a splash with your new knowledge!
To solve this problem, let's start by understanding the equation you provided and then work through the steps together.
The equation you wrote is based on the principle of thermal equilibrium, which states that when two substances reach the same temperature, the heat gained by one substance is equal to the heat lost by the other. In this case, we have the water and the thermometer.
The equation you wrote is:
-0.135(4186)(Tf - 38.7) = 0.034(840)(Tf - 21.6)
Let's break it down step by step:
1. The left side of the equation represents the heat gained by the water.
-0.135(4186) is the specific heat capacity of water (in Joules/gram°C) multiplied by the mass of water (in grams), and (Tf - 38.7) represents the change in temperature of the water.
2. The right side of the equation represents the heat lost by the glass thermometer.
0.034(840) is the specific heat capacity of the glass (in Joules/gram°C) multiplied by the mass of the thermometer (in grams), and (Tf - 21.6) represents the change in temperature of the glass thermometer.
Now, let's solve the equation step by step:
Expanding the equation:
-565.11Tf + 21869.752 = 28.56Tf - 616.896
Combining like terms:
-593.67Tf + 21869.752 = -616.896
Moving the terms to one side:
-593.67Tf = -616.896 - 21869.752
Simplifying:
-593.67Tf = -22486.648
Now, divide both sides of the equation by -593.67 to isolate Tf:
Tf = -22486.648 / -593.67
Calculating:
Tf ≈ 37.9145°C
So, according to the calculations, the original temperature of the water is approximately 37.9145°C.
A 30 g glass thermometer reads 21.6°C before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 38.1°C. What was the original temperature of the water?
Please provide step by step equation and answer