Question

a 400.0 g sample of water is at 30.0 °c. how many joules of energy are required to raise the temperature of the water to 45.0 °c?
628 j
1880 j
25100 j
450 j
question 4
6 pts
how many joules of energy are required to raise the temperature of 150.0 g of water from 15.0 °c to 45.0 °c?
4500 j
18800 j
25400 j
6590 j

Explanation:

Step1: Identify the 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. The specific - heat capacity of water $c = 4.18\ J/(g\cdot^{\circ}C)$.

Step2: Calculate $\Delta T$ for the first question

For the first question, the initial temperature $T_1 = 30.0^{\circ}C$ and the final temperature $T_2 = 45.0^{\circ}C$. So, $\Delta T=T_2 - T_1=45.0 - 30.0=15.0^{\circ}C$, and $m = 400.0\ g$. Then $Q_1=mc\Delta T=400.0\ g\times4.18\ J/(g\cdot^{\circ}C)\times15.0^{\circ}C = 25080\ J\approx25100\ J$.

Step3: Calculate $\Delta T$ for the second question

For the second question, $T_1 = 15.0^{\circ}C$, $T_2 = 45.0^{\circ}C$, so $\Delta T=T_2 - T_1=45.0 - 15.0 = 30.0^{\circ}C$, and $m = 150.0\ g$. Then $Q_2=mc\Delta T=150.0\ g\times4.18\ J/(g\cdot^{\circ}C)\times30.0^{\circ}C=18810\ J\approx18800\ J$.

Answer:

First question: C. 25100 J
Second question: B. 18800 J