Which of the following would require the greatest amount of calories?
Heating
$100\text{g}$ of water from$10\degree\text{C}$ to$50\degree\text{C}$ .
A
- How high must the person climb?
- The acceleration due to gravity is
$\textcolor{#ff5555}{g}$ $\frac{\text{m}}{\text{s}^2}$ and$1$ $\text{food Calorie}$ is$10^3$ $\text{Calories}$ . - Answer in units of
$\text{km}$ .
$Q_j = \frac{\textcolor{#ff5555}{Q}}{1000} \cdot 4186$
$h = \frac{Q_j}{\textcolor{#ff5555}{mg}}$
$h = \frac{4186\textcolor{#ff5555}{Q}}{1000\textcolor{#ff5555}{mg}}$ [solution]
Consider the following statements.
Heat flows from an object at higher temperature to an object at lower temperature; [solution]
Heat flows from an object in liquid state to an object in solid state;
Heat flows from an object with higher thermal energy to an object with lower thermal energy.
A
- If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change?
- Assume the specific heat of lead is
$\textcolor{#ff5555}{c}$ $\frac{\text{J}}{\text{kg}\degree\text{C}}$ . - Answer in units of
$\degree\text{C}$ .
$Q = \frac{\textcolor{#ff5555}{mv}^2}{2}$
$\Delta T = \frac{Q}{\textcolor{#ff5555}{mc}}$
$\Delta T = \frac{\textcolor{#ff5555}{v}^2}{2\textcolor{#ff5555}{c}}$ [solution]
A
- Find the final temperature of the thermometer, assuming no heat flows to the surroundings.
- The specific heat of glass is
$\textcolor{#ff5555}{c_g}$ $\frac{\text{cal}}{\text{g}\degree\text{C}}$ and of water$\textcolor{#ff5555}{c_w}$ $\frac{\text{cal}}{\text{g}\degree\text{C}}$ .
$m_w = \textcolor{#ff5555}{V}$
$T_F = \frac{\textcolor{#ff5555}{mc_gT_t}+\textcolor{#ff5555}{Vc_wT_w}}{\textcolor{#ff5555}{mc_g}+\textcolor{#ff5555}{Vc_w}}$ [solution]
A
- How much water freezes onto the ice? The specific heat of ice is
$\textcolor{#ff5555}{c_i}$ $\frac{\text{cal}}{\text{g}\degree\text{C}}$ and its heat of fusion of is$\textcolor{#ff5555}{L_f}$ $\frac{\text{cal}}{\text{g}}$ - Answer in units of
$\text{g}$ .
$Q_f = Q_i$
$m_f\textcolor{#ff5555}{L_f} = \textcolor{#ff5555}{m_ic_i}(T_f - \textcolor{#ff5555}{T_i})$
$T_f = 0\degree\text{C}$ (freezing point of water)
$m_f = \frac{-\textcolor{#ff5555}{m_ic_iT_i}}{\textcolor{#ff5555}{L_f}}$ [solution]
Which statement is wrong?
Temperature measures the average kinetic energy of random motion, but not other kinds of energy
Adding the same amount of heat to two different objects will produce the same increase in temperature. [solution]
Each substance has its own characteristic specific heat capacity.
When the same amount of heat produces different changes in temperature in two substances of the same mass, we say that they have different specific heat capacities.
Different substances have different thermal properties due to differences in the way energy is stored internally in the substances.
A
- If the final equilibrium state of the mixed system is
$\textcolor{#ff5555}{T_f}$ $\degree\text{C}$ , find the specific heat of the metal. - The specific heat of water is
$\textcolor{#ff5555}{c_w}$ $\frac{\text{J}}{\text{kg}\degree\text{C}}$ . - Answer in units of
$\frac{\text{J}}{\text{kg}\degree\text{C}}$ .
$Q_h + Q_c = 0$
$\textcolor{#ff5555}{m_mc_m}\Delta \textcolor{#ff5555}{T_m} + \textcolor{#ff5555}{m_wc_w}\Delta \textcolor{#ff5555}{T_w} = 0$
$\textcolor{#ff5555}{m_m}c_m(\textcolor{#ff5555}{T_f} - \textcolor{#ff5555}{T_m}) + \textcolor{#ff5555}{m_wc_w}(\textcolor{#ff5555}{T_f} - \textcolor{#ff5555}{T_w}) = 0$
$\therefore c_m = \frac{-\textcolor{#ff5555}{m_wc_w}(\textcolor{#ff5555}{T_f} - \textcolor{#ff5555}{T_w})}{\textcolor{#ff5555}{m_m}(\textcolor{#ff5555}{T_f} - \textcolor{#ff5555}{T_m})}$ [solution]
Three liquids are at temperatures of
- Find the equilibrium temperature when equal masses of the first and third are mixed.
- Answer in units of
$\degree\text{C}$ .
Let
$a = \frac{(\textcolor{#ff5555}{T_a} - \textcolor{#ff5555}{T_{ab}})}{\textcolor{#ff5555}{T_{ab}} - \textcolor{#ff5555}{T_b}}$
$c_b = a c_a$ Let
$b = \frac{(\textcolor{#ff5555}{T_b} - \textcolor{#ff5555}{T_{bc}})}{\textcolor{#ff5555}{T_{bc}} - \textcolor{#ff5555}{T_c}}$
$c_c = b c_b = b a c_a$
$m_ac_a(T_f - \textcolor{#ff5555}{T_a}) + m_cc_c(T_f-\textcolor{#ff5555}{T_c}) = 0$
$c_aT_f + c_cT_f = c_a\textcolor{#ff5555}{T_a} + c_c\textcolor{#ff5555}{T_c}$
$T_f = \frac{c_a\textcolor{#ff5555}{T_a}+c_c\textcolor{#ff5555}{T_c}}{c_a+c_c}$
$T_f = \frac{c_a\textcolor{#ff5555}{T_a}+ba c_a\textcolor{#ff5555}{T_c}}{c_a+ba c_a}$
$T_f = \frac{\textcolor{#ff5555}{T_a}+ba \textcolor{#ff5555}{T_c}}{1+ba}$ [solution] [do not expand$a$ and$b$ ]
When water freezes
there is no heat exchange with the surroundings.
heat is absorbed from the surroundings.
the temperature of the water increases.
the temperature of the water decreases.
heat is given off to the surroundings. [solution]
A jar of tea is placed in sunlight until it reaches an equilibrium temperature of
- At the time at which the temperature of the tea is
$\textcolor{#ff5555}{T_f}$ $\degree\text{C}$ , find the mass of the remaining ice in the jar. - The specific heat of water is
$\textcolor{#ff5555}{c_w}$ $\frac{\text{J}}{\text{kg}\degree{C}}$ . - Assume the specific heat capacity of the tea is to be that of pure liquid water.
- Answer in units of
$\text{g}$ .
The brick wall (of thermal conductivity
- How much heat flows through the wall in a(n)
$\textcolor{#ff5555}{t}$ $\text{h}$ period when the average inside and outside temperatures are, respectively,$\textcolor{#ff5555}{T_i}$ $\degree\text{C}$ and$\textcolor{#ff5555}{T_o}$ $\degree\text{C}$ ? - Answer in units of
$\text{MJ}$ .
An iron nail is driven into a block of ice by a single blow of a hammer. The hammerhead has a mass of
- How much ice melts? Assume the temperature of both the ice and the nail is
$0$ $\degree\text{C}$ before and after. The heat of fusion of ice is$\textcolor{#ff5555}{L_f}$ $\frac{\text{cal}}{\text{g}}$ . - Answer in units of
$\text{g}$
How much energy is required to change a
- The specific heat of ice is
$\textcolor{#ff5555}{c_i}$ $\frac{\text{J}}{\text{kg}\degree\text{C}}$ - The specific heat of water is
$\textcolor{#ff5555}{c_w}$ $\frac{\text{J}}{\text{kg}\degree\text{C}}$ - The specific heat of ice is
$\textcolor{#ff5555}{c_s}$ $\frac{\text{J}}{\text{kg}\degree\text{C}}$ - The heat of fusion is
$\textcolor{#ff5555}{L_f}$ $\frac{\text{J}}{\text{kg}}$ - The heat of vaporization is
$\textcolor{#ff5555}{L_v}$ $\frac{\text{J}}{\text{kg}}$
$Q_t = \sum{Q}$ .$Q_t = Q_i + Q_f + Q_w + Q_v + Q_s$ .$Q_t = -\textcolor{#ff5555}{mc_iT_i} + \textcolor{#ff5555}{mL_f} + 100\textcolor{#ff5555}{mc_w} + \textcolor{#ff5555}{mL_v} + \textcolor{#ff5555}{mc_s}(\textcolor{#ff5555}{T_f} - 100)$