A sample of metal has a mass of 1.75 kg and a specific heat of 0.115 cal/g oC. What is the temperature change of the metal after 625 calories of heat are added?
My answer is 3 oC.
Just want to make sure is right and my equation is set up right.
Why are you throwing away the rest of the number? I'm sure they showed on your calculator but you ignored them. You're allowed 3 places and you reported only 1.
My answer is 3.10559 which I would round to 3.11 to three s.f. Your set up must be ok.
To determine the temperature change, you can use the formula:
q = m * c * ΔT
where q is the heat energy added, m is the mass of the metal, c is the specific heat, and ΔT is the change in temperature.
Using the given values:
q = 625 calories
m = 1.75 kg (since 1 kg = 1000 g, 1.75 kg = 1750 g)
c = 0.115 cal/g°C
Rearranging the formula and solving for ΔT:
ΔT = q / (m * c)
ΔT = 625 cal / (1750 g * 0.115 cal/g°C)
Converting grams to kilograms:
ΔT = 625 cal / (1.75 kg * 0.115 cal/g°C)
Calculating ΔT:
ΔT = 625 cal / 0.20125 cal/°C
ΔT ≈ 3108 °C
Therefore, the temperature change of the metal after adding 625 calories of heat is approximately 3108 °C, not 3 °C.
To calculate the temperature change of the metal, we can use the formula:
q = mcΔT
Where q is the heat added (in calories), m is the mass of the metal (in grams), c is the specific heat of the metal (in cal/g oC), and ΔT is the temperature change of the metal (in oC).
Let's convert the mass from kilograms to grams:
1.75 kg = 1.75 * 1000 = 1750 grams
Now we can substitute the values into the formula:
625 calories = 1750 grams * 0.115 cal/g oC * ΔT
Next, rearrange the equation to solve for ΔT:
ΔT = 625 calories / (1750 grams * 0.115 cal/g oC)
Perform the calculation:
ΔT = 625 / (1750 * 0.115)
ΔT ≈ 3.03 oC
So, the temperature change of the metal after 625 calories of heat are added is approximately 3.03 oC. Therefore, your answer of 3 oC is correct, rounded to the nearest whole number.