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.

Consider an ideal gas-turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle, assuming (a) no regenerator is used and (b) a regenerator with 75 percent effectiveness is used. Use variable specific heats.

Materials A and B have equal densities, but A has a larger specific heat than B. You have 100 g cubes of each material. Cube A, initially at $0^{\circ} \mathrm{C}$, is placed in good thermal contact with cube B, initially at $200^{\circ} \mathrm{C}$. The cubes are inside a well-insulated container where they don't interact with their surroundings. Is their final temperature greater than, less than, or equal to $100^{\circ} \mathrm{C}$? Explain.

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

A container filled with 45 kg of liquid water at 95$^\circ{}$C is placed in a 90-m^3 room that is initially at 12$^\circ{}$C. Thermal equilibrium is established after a while as a result of heat transfer between the water and the air in the room. Using constant specific heats, determine (a) the final equilibrium temperature, (b) the amount of heat transfer between the water and the air in the room, and (c) the entropy generation. Assume the room is well sealed and heavily insulated.

A $1.00$-mole sample of ammonia at $14.0 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$ in a cylinder fitted with a movable piston expands against a constant external pressure of $1.00 \mathrm{~atm}$. At equilibrium, the pressure and volume of the gas are $1.00 \mathrm{~atm}$ and $23.5 \mathrm{~L}$, respectively.
(a) Calculate the final temperature of the sample.
(b) Calculate $q, w$, and $\Delta U$ for the process. The specific heat of ammonia is $0.0258 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}$.

Consider a simple Brayton cycle using air as the working fluid; has a pressure ratio of 12; has a maximum cycle temperature of $600^\circ C;$ and operates the compressor inlet at 100 kPa and $15^\circ C.$ Which will have the greatest impact on the back-work ratio: a compressor isentropic efficiency of 80 percent or a turbine isentropic efficiency of 80 percent? Use constant specific heats at room temperature.

Consider the following data:

When these two metals are placed in contact,the following will take place? Heat will flow from Cu to Al because Cu has a larger mass.

In one box of nails, there are 75 iron nails weighing 0.250 lb. The density of iron is 7.86 $g/cm^3$. The specific heat of iron is 0.452 J/g $\degree$ C. The melting point of iron is 1535 $\degree$ C. The heat of fusion for iron is 272 J/g. How much heat, in joules, must be added to the nails in the box to raise their temperature from 16 $\degree$ C to 125 $\degree$ C?

A turbojet is flying with a velocity of $275 \mathrm{~m} / \mathrm{s}$ at an altitude of $6100 \mathrm{~m}$, where the ambient conditions are $50 \mathrm{~kPa}$ and $-12^{\circ} \mathrm{C}$. The pressure ratio across the compressor is 13 , and the temperature at the turbine inlet is $1330 \mathrm{~K}$. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine $(a)$ the pressure at the turbine exit, $(b)$ the velocity of the exhaust gases, and $(c)$ the propulsive efficiency.

Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 70 MW, assuming both the compressor and the turbine have an isentropic efficiency of (a ) 100 percent and (b ) 85 percent. Assume constant specific heats at room temperature.

A 75.0-g sample of a metal is placed in boiling water until its temperature is $100.0^{\circ} \mathrm{C}$. A calorimeter contains 100.00 g of water at a temperature of $24.4^{\circ} \mathrm{C}$. The metal sample is removed from the boiling water and immediately placed in water in the calorimeter. The final temperature of the metal and water in the calorimeter is $34.9^{\circ} \mathrm{C}$. Assuming that the calorimeter provides perfect insulation, what is the specific heat of the metal?

Why are the back work ratios relatively high in gas-turbine engines?

The largest of the Great Lakes, Lake Superior, contains $1.20 \times 10^{16} \mathrm{kg}$ of fresh water, which has a specific heat capacity of $4186 \mathrm{J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ and a latent heat of fusion of $3.33 \times 10^{5} \mathrm{J} / \mathrm{kg}$. How much energy would be needed to increase the temperature of Lake Superior by $1.0^{\circ} \mathrm{C}$?