Question

A piece of unknown substance weighs 44.7 g and requires 2110 J to increase its temperature from 23.2 °C to 89.6 °C.

What is the specific heat capacity of the unknown substance?

a) 0.37 J/g°C
b) 4.18 J/g°C
c) 2.82 J/g°C
d) 1.95 J/g°C

Answer 1

To determine the specific heat capacity of the substance, the formula Q = mcΔT is used, where Q is the heat energy, m is the mass, ΔT is the change in temperature, and c is the specific heat capacity. Using the given data, the specific heat capacity is calculated to be approximately 0.711 J/g°C, which does not match any of the provided multiple choice options.

Step-by-step explanation:

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

Q = mcΔT

Where:

• Q is the amount of heat energy in joules
• m is the mass of the substance in grams
• c is the specific heat capacity in J/g°C
• ΔT is the change in temperature in degrees Celsius (final temperature - initial temperature)

Rearranging the formula to solve for c:

c = Q / (mΔT)

Given:

• Q = 2110 J
• m = 44.7 g
• ΔT = 89.6°C - 23.2°C = 66.4°C

Plugging the values into the equation:

c = 2110 J / (44.7 g × 66.4°C)

c = 2110 J / 2968.48 g°C

c = 0.711 J/g°C

Comparing this result to the multiple choice options, we find that none of the options exactly match this value.