Question

which substance would you expect to take more energy to heat up, substance a with a specific heat capacity of 1.75 j/(kg °c) or substance b with a specific heat capacity of 2.58 j/(kg °c) and why? you have 200 grams of each substance and you heat the object from 15.0 °c to 45.0 °c. substance b because it has a larger specific heat capacity. cannot be determined because we dont know the mass. substance a because it has a smaller specific heat capacity than substance b. both will take the same amount of energy to heat up.

Explanation:

Step1: Recall heat - energy formula

The formula for heat energy is $Q = mc\Delta T$, where $Q$ is the heat energy, $m$ is the mass, $c$ is the specific - heat capacity, and $\Delta T$ is the change in temperature.

Step2: Identify given values

We have $m_A=m_B = 200\ g=0.2\ kg$, $\Delta T_A=\Delta T_B=45.0 - 15.0=30.0^{\circ}C$, $c_A = 1.75\ J/(kg\cdot^{\circ}C)$ and $c_B = 2.58\ J/(kg\cdot^{\circ}C)$.

Step3: Calculate heat energy for substance A

$Q_A=m_A c_A\Delta T_A=(0.2\ kg)\times(1.75\ J/(kg\cdot^{\circ}C))\times30.0^{\circ}C = 10.5\ J$.

Step4: Calculate heat energy for substance B

$Q_B=m_B c_B\Delta T_B=(0.2\ kg)\times(2.58\ J/(kg\cdot^{\circ}C))\times30.0^{\circ}C = 15.48\ J$.

Answer:

Substance B because it has a larger specific - heat capacity.