I am confused as to how to solve this problem. Can someone please tell me the steps? I know SH = heat/ mass x change in temp.
What is the specific heat of a metal if 7.74 × 103 J of energy is required to warm a 75.0 g sample of the metal from 10 °C to 125 °C?
THanks
-MC
q = mass x s.h. x (Tfinal-Tinitial)
7.74E3 = 75.0 x s.h. x (125-10)
Solve for s.h.
To find the specific heat (SH) of the metal, you will need to use the equation SH = heat / (mass x change in temperature). Here are the steps to solve this problem:
Step 1: Identify the given values:
- Heat (H) = 7.74 × 10^3 J
- Mass (m) = 75.0 g
- Change in temperature (ΔT) = (final temperature - initial temperature) = (125 °C - 10 °C)
Step 2: Calculate the change in temperature (ΔT):
ΔT = 125 °C - 10 °C = 115 °C
Step 3: Calculate the specific heat (SH):
SH = H / (m x ΔT)
= 7.74 × 10^3 J / (75.0 g x 115 °C)
Step 4: Convert the units to match:
It is important to make sure that the units used in the calculation are consistent. In this case, we need to convert the mass from grams to kilograms and the temperature from Celsius to Kelvin.
To convert grams to kilograms, divide the mass by 1000:
75.0 g ÷ 1000 = 0.075 kg
To convert Celsius to Kelvin, add 273.15:
115 °C + 273.15 = 388.15 K
Step 5: Substitute the values into the equation and solve:
SH = 7.74 × 10^3 J / (0.075 kg x 388.15 K)
Now, you can calculate the specific heat of the metal using a calculator or by solving the arithmetic.
I hope this helps! Let me know if you have any further questions.