When $20.0 \mathrm{~g}$ of mercury are heated from $10.0^{\circ} \mathrm{C}$ to $20.0^{\circ} \mathrm{C}$, $27.6 \mathrm{~J}$ of energy are absorbed. What is the specific heat of mercury?

(a) $0.726 \mathrm{~J}/\mathrm{g}^{\circ} \mathrm{C}$
(b) $0.138 \mathrm{~J}/\mathrm{g}^{\circ} \mathrm{C}$
(c) $2.76 \mathrm{~J}/\mathrm{g}^{\circ} \mathrm{C}$
(d) no correct answer given

To help prevent frost damage, $4.00 \mathrm{~kg}$ of water at $0^{\circ} \mathrm{C}$ is sprayed onto a fruit tree. $(a)$ How much heat transfer occurs as the water freezes? $(b)$ How much would the temperature of the $200 \mathrm{~kg}$ tree decrease if this amount of heat transferred from the tree? Take the specific heat to be $3.35 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$, and assume that no phase change occurs in the tree.

1.5 kg of liquid water initially at 12$^\circ{}$C is to be heated to 95$^\circ{}$C in a teapot equipped with an 800-W electric heating element inside. The specific heat of water can be taken to be 4.18 kJ/kgK, and the heat loss from the water during heating can be neglected. The time it takes to heat water to the desired temperature is (a) 5.9 min (b) 7.3 min (c) 10.8 min (d) 14.0 min (e) 17.0 min

An $825\text{~g}$ iron block is heated to $352{ }^{\circ} \mathrm{C}$ and placed in an insulated container (of negligible heat capacity) containing $40.0 \mathrm{~g}$ of water at $20.0^{\circ} \mathrm{C}$. What is the equilibrium temperature of this system? If your answer is $100^{\circ} \mathrm{C}$, find the amount of water that has vaporized. The average specific heat of iron over this temperature range is $560 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$.

The temperature of an incompressible substance of mass $m$ and specific heat $c$ is reduced from $T_0$ to $T\left(<T_0\right)$ by a refrigeration cycle. The cycle receives energy by heat transfer at $T$ from the substance and discharges energy by heat transfer at $T_0$ to the surroundings. There are no other heat transfers. Plot $\left(W_{\min } / m c T_0\right)$ versus $T / T_0$ ranging from $0.8$ to $1.0$, where $W_{\min }$ is the minimum theoretical work input required.

Given that the specific heat capacities of ice and steam are $2.06 \mathrm{~J} / \mathrm{g}{ }^{\circ} \mathrm{C}$ and $2.03 \mathrm{~J} / \mathrm{g}{ }^{\circ} \mathrm{C}$, respectively, and considering the information about water given in Exercise 16, calculate the total quantity of heat evolved when $10.0 \mathrm{~g}$ of steam at $200 .^{\circ} \mathrm{C}$ is condensed, cooled, and frozen to ice at $-50 .{ }^{\circ} \mathrm{C}$.

A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.

A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.

A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in $^ { \circ } \mathrm { C } / \mathrm { min }$) will its temperature increase if its mass is 20.0 kg and it has a specific heat of $0.300 \mathrm { kcal } / \mathrm { kg } \cdot ^ { \circ } \mathrm { C }$, assuming no heat escapes?

Water has a specific heat capacity nearly 9 times that of iron. Suppose a $50-\mathrm{g}$ pellet of iron at a temperature of $200^{\circ} \mathrm{C}$ is dropped into $50 \mathrm{~g}$ of water at a temperature of $20^{\circ} \mathrm{C}$. When the system reaches thermal equilibrium, its temperature will be
A. closer to $20^{\circ} \mathrm{C}$.
B. closer to $200^{\circ} \mathrm{C}$.
C. halfway between the two initial temperatures.

A portable coffee heater supplies a potential difference of 12.0 V across a Nichrome heating element with a resistance of $2.00 \Omega$. How many minutes would it take to heat 1.00 kg of coffee from $20.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$ with this heater? Coffee has a specific heat of $4184 \mathrm{J} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)$. Neglect any energy losses to the environment.

The compression ratio of an air-standard Otto cycle is $9.5$. Prior to the isentropic compression process, the air is at $100\ \mathrm{kPa}, 35^{\circ} \mathrm{C}$, and $600 \mathrm{~cm}^3$. The temperature at the end of the isentropic expansion process is $800 \mathrm{~K}$. Using specific heat values at room temperature, find $(a)$ the highest temperature and pressure in the cycle; $(b)$ the amount of heat transferred in, in $\mathrm{kJ} ;(c)$ the thermal efficiency; and $(d)$ the mean effective pressure.

A Three 45-g ice cubes at $0^{\circ} \mathrm{C}$ are dropped into $5.00 \times 10^2 \mathrm{~mL}$ of tea to make iced tea. The tea was initially at $20.0^{\circ} \mathrm{C}$; when thermal equilibrium was reached, the final temperature was $0^{\circ} \mathrm{C}$. How much of the ice melted, and how much remained floating in the beverage? Assume the specific heat capacity of tea is the same as that of pure water.

Air enters the compressor of a gas-turbine engine at $300 \mathrm{~K}$ and $100\ \mathrm{kPa}$, where it is compressed to $700\ \mathrm{kPa}$ and $580 \mathrm{~K}$. Heat is transferred to the air in the amount of $950 \mathrm{~kJ} / \mathrm{kg}$ before it enters the turbine. For a turbine efficiency of $86$ percent, find $(a)$ the fraction of the turbine work output used to drive the compressor and $(b)$ the thermal efficiency. Use constant specific heat at room temperature.