Question

A sample of an unknown substance has a mass of 0.158 kg. If 2,510.0 J of heat is required to heat the substance from 32.0°C to 61.0°C, what is the specific heat of the substance?

1) 0.171 J/(g°C)
2) 0.548 J/(g°C)
3) 15.9 J/(g°C)
4) 86.6 J/(g°C)

Answer 1

The specific heat of the substance is calculated using the formula c = Q / (mΔT), which results in a value of approximately 0.548 J/g°C, corresponding to option 2 in the choices provided.

Step-by-step explanation:

To calculate the specific heat of the substance, we use the formula:

Q = mcΔT

where
Q = heat energy (in joules),
​m = mass of the substance (in grams),
​c = specific heat capacity (in J/g°C),
ΔT = change in temperature (in °C).

We rearrange the formula to solve for c:

c = Q / (mΔT)

Given the problem:
Q = 2,510.0 J,
Initial Temperature = 32.0°C,
Final Temperature = 61.0°C,
ΔT = Final Temperature - Initial Temperature = 61.0°C - 32.0°C = 29.0°C.
m = 0.158 kg = 158 g (since 1 kg = 1000 g).

Now we plug these values into our rearranged formula:

c = 2,510.0 J / (158 g × 29.0°C) = 2,510.0 J / 4,582 g°C ≈ 0.548 J/g°C

Therefore, the specific heat of the substance is 0.548 J/(g°C), which corresponds to option 2 in the provided choices.