Question

two containers of water and their starting conditions are shown below. how will the temperatures of the water in the containers compare if an equal amount of heat is absorbed by each container of water without boiling? a. both water temperatures will increase by the same amount. b. both water temperatures will decrease, but container bs will decrease more. c. both water temperatures will increase, but container as will increase more. d. both water temperatures will increase, but container bs will increase more.

Explanation:

Step1: Recall heat - mass - temperature change relation

The heat absorbed $Q$ is given by the formula $Q = mc\Delta T$, where $m$ is the mass, $c$ is the specific - heat capacity (constant for water in this case), and $\Delta T$ is the change in temperature. Since density of water is constant, mass $m$ is proportional to volume $V$. Container A has a volume $V_A=1000\ mL$ and container B has a volume $V_B = 250\ mL$, so $m_A>m_B$.

Step2: Solve for $\Delta T$

We can re - arrange the formula $Q = mc\Delta T$ to $\Delta T=\frac{Q}{mc}$. Given that $Q$ is the same for both containers and $c$ is the same (specific heat of water), $\Delta T$ is inversely proportional to $m$. Since $m_A>m_B$, $\Delta T_A<\Delta T_B$.

Answer:

D. Both water temperatures will increase, but container B's will increase more.