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? Use q = mcΔt.

a. 0.171 J/(g°C)
b. 0.548 J/(g°C)
c. 15.9 J/(g°C)
d. 86.6 J/(g°C)

Answer 1

The specific heat of the substance is 0.548 J/(g°C), found by using the formula q = mcΔt with the mass converted to grams and the change in temperature calculated as the difference between the final and initial temperatures.

Step-by-step explanation:

To find the specific heat of the substance, we can use the formula q = mcΔt, where q is the heat energy transferred, m is the mass of the substance, and Δt is the change in temperature. In this case, we will first convert the mass from kilograms to grams (1 kg = 1000 g), then plug the given values into the equation to solve for specific heat c.

First, convert the mass: 0.158 kg * 1000 g/kg = 158 g.

Next, calculate the change in temperature: Δt = 61.0°C - 32.0°C = 29.0°C.

We are given that q = 2,510.0 J. With all values in place, we can rearrange the equation to solve for c:

c = q / (m * Δt) = 2,510.0 J / (158 g * 29.0°C) = 0.548 J/(g°C)

Thus, the specific heat of the substance is 0.548 J/(g°C), which corresponds to option b.