How many calories are required to heat 25.0 g of platinum from 24.5 °C to 75°C (specific heat of platinum = 0.139 J/gK)?
1. 47 cal
2. 42 cal
3. 48 cal
4. 20 cal
5. 80 cal
Thank you.
q = m*c*delta T.
42cal
48
Well, that's a hot question! Let's do some calculations, shall we?
First, we need to find the change in temperature: ΔT = 75°C - 24.5°C = 50.5°C.
Now, we can calculate the amount of energy required using the formula: q = m × C × ΔT, where q is the energy, m is the mass, C is the specific heat, and ΔT is the change in temperature.
Plugging in the values: q = 25.0 g × 0.139 J/gK × 50.5°C = 174.37875 J.
Converting it into calories by dividing by 4.184 J/cal, we get q ≈ 41.66 cal.
So, it looks like the closest option is 42 cal (option 2). Stay cool!
To calculate the amount of calories required to heat a substance, you can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of heat energy (in calories),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/gK),
ΔT is the change in temperature (in °C).
Given:
m = 25.0 g (mass of platinum),
c = 0.139 J/gK (specific heat of platinum),
ΔT = 75 °C - 24.5 °C = 50.5 °C (change in temperature).
Now, let's calculate the amount of heat energy required:
Q = (25.0 g) * (0.139 J/gK) * (50.5 °C)
Q = 87.41 J
To convert this value from joules to calories, divide by the conversion factor of 4.184 J/cal:
Q = 87.41 J / 4.184 J/cal
Q ≈ 20.9 cal
Based on the calculation, the amount of calories required to heat 25.0 g of platinum from 24.5 °C to 75°C is approximately 20.9 cal.
Therefore, option 4, 20 cal, is the closest answer.